<PAGE>
 
      As filed with the Securities and Exchange Commission on May 20, 1998
                                                          Registration No. 333-
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                                 --------------
                                    FORM S-8
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933
                                 --------------

                            APEX SILVER MINES LIMITED
               (Exact Name of Issuer as Specified in its Charter)

          Cayman Islands                                       Not Applicable
 (State or Other Jurisdiction of                               (I.R.S. Employer
 Incorporation or Organization)                              Identification No.)

                         Caledonian House, Ground Floor
                                   Mary Street
                            George Town, Grand Cayman
                       Cayman Islands, British West Indies
                                 (345) 949-0050
                    (Address of Principal Executive Offices)
                                 --------------

                            APEX SILVER MINES LIMITED
                          EMPLOYEES' SHARE OPTION PLAN

                            APEX SILVER MINES LIMITED
                             NON-EMPLOYEE DIRECTORS'
                                SHARE OPTION PLAN

                            APEX SILVER MINES LIMITED
                               NON-QUALIFIED STOCK
                                OPTION AGREEMENTS
                            (Full Title of the Plans)
                                 --------------

                                Thomas S. Kaplan
                             Chief Executive Officer
                          Apex Silver Mines Corporation
                         1700 Lincoln Street, Suite 3050
                             Denver, Colorado 80203
                                 (303) 839-5060
                     (Name and Address of Agent for Service)
   Telephone Number, Including Area Code, of Agent for Service: (303) 839-5060

<TABLE>
<CAPTION>


                                          CALCULATION OF REGISTRATION FEE
============================= ===================== ======================== ======================= ==========================
      Title of Shares              Amount to           Proposed Maximum         Proposed maximum             Amount of
      to be Registered          be Registered(1)      Offering Price Per       Aggregate Offering        Registration Fee
                                                             Share                  Price(2)
----------------------------- --------------------- ------------------------ ----------------------- --------------------------
<S>                           <C>                    <C>                     <C>                     <C>    

 Ordinary Shares (par value    3,040,625 Ordinary    Not Applicable           $33,212,744             $9,798
 $.01 per share)               Shares
============================= ===================== ======================== ======================= ==========================
</TABLE>

(1)  There are also registered hereunder such additional indeterminate number of
     ordinary shares, par value $0.01 per share (the "Ordinary Shares"), as may
     be issued as a result of the antidilution provisions of the Apex Silver
     Mines Limited Employees' Share Option Plan (the "Employees' Share Option
     Plan"), the Apex Silver Mines Limited Non-Employee Directors' Share Option
     Plan (the "Non-Employee Directors' Share Option Plan") and the Apex Silver
     Mines Limited Non-Qualified Stock Option Agreements (the "Non-Qualified
     Stock Option Agreements").

(2)  Calculated on the basis of (i) 455,625 Ordinary Shares at $8.00 per
     Ordinary Share having an aggregate price of $3,645,000, pursuant to Rule
     457(h)(1) of the Securities Act of 1933, as amended (the "Act"), which is
     the aggregate offering price of certain of the Ordinary Shares subject to
     outstanding options under the Employees' Share Option Plan and all of the
     Non-Qualified Stock Option Agreements, (ii) 54,081 Ordinary Shares at $11
     3/16 per Ordinary Share having an aggregate price of $605,031, pursuant to
     Rule 457(h)(1) of the Act, which is the aggregate offering price of certain
     of the Ordinary Shares subject to outstanding options under the Employees'
     Share Option Plan and (iii) with respect to the remaining 2,530,919
     Ordinary Shares registered hereunder, using the average of the high and low
     prices reported on the American Stock Exchange on May 14, 1998, which is
     $11.44, having an aggregate offering price of $28,953,713, pursuant to Rule
     457(h)(1) and Rule 457(c) of the Act.

================================================================================
<PAGE>
 
                                   STATEMENT
                                   ---------

     This Registration Statement on Form S-8 is being filed with the Securities
and Exchange Commission (the "Commission") by Apex Silver Mines Limited, a
Cayman Islands Corporation (the "Company"), in order to register (i) 2,000,000
Ordinary Shares that will be available for issuance under the Employees' Share
Option Plan, (ii) 1,000,000 additional Ordinary Shares that will be available
for issuance under the Non-Employee Directors' Share Option Plan, all of which
may be issued upon the exercise of options granted under such plans, and (iii)
40,625 additional Ordinary Shares which may be issued by the Company pursuant to
the exercise of options granted in Non-Qualified Stock Option Agreements to each
of the seven non-employee directors of the Company.

                                       2
<PAGE>
 
                                    PART I

Item 1.  PLANS INFORMATION.

         Not included pursuant to Form S-8 instructions.

Item 2.  REGISTRANT INFORMATION AND PLANS ANNUAL INFORMATION.

         Not included pursuant to Form S-8 instructions.

                                    PART II

Item 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE.

     The Company hereby incorporates herein by reference the following
     documents:

     (1)  The description of the Company's Ordinary Shares contained in the
          Registration Statement on Form S-1 filed with the Securities and
          Exchange Commission (the "Commission") on August 29, 1997,
          Registration No. 333-34685, including amendments thereto and any
          report filed for the purpose of updating such description (the
          "Registration Statement");

     (2)  The Company's Annual Report on Form 10-K for the year ended December
          31, 1997, including portions of the Company's proxy statement dated
          April 15, 1998 relating to the Company's 1998 annual meeting of
          shareholders, which are incorporated therein by reference;

     (3)  The Company's proxy statement dated April 15, 1998;

     (4)  The Company's quarterly report on Form 10-Q for the quarter ended
          March 31, 1998; and

     (5)  All reports filed pursuant to Section 13(a) or 15(d) of the Securities
          Exchange Act of 1934, as amended (the "Exchange Act"), subsequent to
          the date of this filing.

     In addition, all documents filed by the Company pursuant to Sections 13(a),
13(c), 14 and 15(d) of the Exchange Act subsequent to the date of this
Registration Statement and prior to the filing of a post-effective amendment
which indicates that all securities offered herein have been sold or which
deregisters all securities then remaining unsold shall be deemed to be
incorporated herein by reference and to be a part hereof from the respective
date of filing of each such document.

Item 4.  DESCRIPTION OF SECURITIES.

         Not applicable.

Item 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL.

         Not applicable.

Item 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS.

     Cayman Islands law does not limit the extent to which a company's Articles
of Association may provide for the indemnification of officers and directors,
except to the extent that such provision may be held by the Cayman Islands
courts to be contrary to public policy (for instance, for purporting to provide
indemnification against the consequences of committing a crime). In addition, an
officer or director may not be indemnified for fraud or willful default.

                                       3
<PAGE>
 
     The Company's Articles contain provisions providing for the indemnity by
the Company of an officer, director, consultant, employee or agent of the
Company for threatened, pending or contemplated actions, suits or proceedings,
whether civil, criminal, administrative or investigative (including, without
limitation, an action by or the right of the company), brought against such
indemnified person by reason of the fact that such person was an officer,
director, consultant, employee or agent of the Company. In addition, the board
of directors may authorize the Company to purchase and maintain insurance on
behalf of any such person against any liability asserted against him and
incurred by him in any such capacity, or arising out of his status as such,
whether or not the company would have the power to indemnify him against such
liability under the provisions of the Articles.

     The Company also purchases directors and officers liability insurance from
third parties for its directors and officers. The Company's Article's provide
that directors and officers of the Company shall have no liability (i) for the
acts, receipts, neglects, defaults or omissions of any other such director or
officer or agent of the Company or (ii) by reason of his having joined in any
receipt for money not received by him personally or (iii) for any loss on
account of defect of title to any property of the Company or (iv) on account of
the insufficiency of any security in or upon which any money of the Company
shall be invested or (v) for any loss incurred through any bank, broker or other
agent or (vi) for any loss occasioned by any negligence, default, breach of
duty, breach of trust, error of judgment or oversight on his part of (vii) for
any loss, damage or misfortune whatsoever which may happen in or arise from the
execution or discharge of the duties, powers, authorities, or discretions of his
office or in relation thereto, unless the same shall happen through his own
dishonesty.

Item 7.  EXEMPTION FROM REGISTRATION CLAIMED.

         Not applicable.

Item 8.  EXHIBITS.

Exhibit No.     Description of Exhibits
----------      -----------------------

 4.1            Apex Silver Mines Limited Employees' Share Option Plan*

 4.2            Apex Silver Mines Limited Non-Employee Directors' Share Option
                Plan*

 4.3            Form of Apex Silver Mines Limited Non-Qualified Stock Option
                Agreement

 5.1            Opinion of W. S. Walker & Company regarding the legality of the
                Ordinary Shares being registered (Cayman Islands law)

23.1            Consent of W.S. Walker & Company (included as part of Exhibit
                5.1)

23.2            Consent of Price Waterhouse LLP

24.1            Power of Attorney (included on the signature page of this
                registration statement)

- - - - - - - - - - -

*incorporated by reference from Registrant's Form S-1 Registration Statement
 (file No. 333-34685), effective November 25, 1997.

Item 9.  UNDERTAKINGS

(a)      The undersigned hereby undertakes:

         (1)  to file, during any period in which offers or sales are being
              made, a post-effective amendment to this registration statement:

              (i)  to include any prospectus required by Section 10(a)(3) of the
                   Securities Act of 1933 (the "Securities Act");

                                       4

<PAGE>
 
          (ii)  to reflect in the prospectus any facts or events arising after
                the effective date of the registration statement (or the most
                recent post-effective amendment thereof) which, individually or
                in the aggregate, represent a fundamental change in the
                information set forth in the registration statement; and

          (iii) to include any material information with respect to the plan of
                distribution not previously disclosed in the registration
                statement or any material change to such information in the
                registration statement;

     provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) do not apply if
     the information to be included in a post-effective amendment by those
     paragraphs is contained in periodic reports filed by the registrant
     pursuant to Section 13 or Section 15(d) of the Exchange Act that are
     incorporated by reference in the registration statement.

     (2)  that, for the purpose of determining any liability under the
          Securities Act, each such post-effective amendment shall be deemed to
          be a new registration statement relating to the securities offered
          therein, and the offering of such securities at that time shall be
          deemed to be the initial bona fide offering thereof; and

     (3)  to remove from registration by means of a post-effective amendment any
          of the securities being registered which remain unsold at the
          termination of the offering.

(b)  The undersigned registrant hereby undertakes that, for purposes of
     determining any liability under the Securities Act, each filing of the
     registrant's Annual Report pursuant to Section 13(a) or Section 15(d) of
     the Exchange Act (and, where applicable, each filing of an employee benefit
     plan's Annual Report pursuant to Section 15(d) of the Exchange Act) that is
     incorporated by reference in the registration statement shall be deemed to
     be a new registration statement relating to the securities offered therein,
     and the offering of such securities at that time shall be deemed to be the
     initial bona fide offering thereof.

(c)  Insofar as indemnification for liabilities arising under the Securities Act
     may be permitted to directors, officers and controlling persons of the
     registrant pursuant to the foregoing provisions, or otherwise, the
     registrant has been advised that in the opinion of the Commission such
     indemnification is against public policy as expressed in the Act and is,
     therefore, unenforceable. In the event that a claim for indemnification
     against such liabilities (other than the payment by the registrant of
     expenses incurred or paid by a director, officer or controlling person of
     the registrant in the successful defense of any action, suit or proceeding)
     is asserted by such director, officer or controlling person in connection
     with the securities being registered, the registrant will, unless in the
     opinion of its counsel the matter has been settled by controlling
     precedent, submit to a court of appropriate jurisdiction the question
     whether such indemnification by it is against public policy as expressed in
     the Act and will be governed by the final adjudication of such issue.

                                       5
<PAGE>
 
                                   SIGNATURES

     Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this registration
statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in New York, New York, on this 14th day of May, 1998.

                                                 APEX SILVER MINES LIMITED


                                                 By: /s/ Thomas S. Kaplan
                                                    --------------------------

                                                 Name:  Thomas S. Kaplan
                                                 Title: Chairman of the Board


                                POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that each person whose signature appears
below constitutes and appoints Thomas S. Kaplan and Keith R. Hulley and each of
them severally, his true and lawful attorneys-in-fact and agents, with full
power of substitution and resubstitution, for him and in his name, place and
stead, in any and all capacities, to sign any and all amendments (including
post-effective amendments) to this registration statement, and to file the same,
with all exhibits thereto, and other documents in connection therewith, with the
Securities and Exchange Commission, granting unto said attorneys-in-fact and
agents, and each of them, full power and authority to do and perform each and
every act and thing requisite or necessary to be done in and about the premises,
as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents or either of
them, or their or his or her substitute or substitutes, may lawfully do or cause
to be done by virtue hereof.

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.


<TABLE>
<S>                                         <C>                                <C>   

Signature                                   Title                               Date
---------                                   -----                               ----


/s/ Thomas S. Kaplan                        Chairman of the Board               May 14, 1998
----------------------------  
Thomas S. Kaplan


/s/ Harry M. Conger                         Director                            May 14, 1998
-----------------------------
Harry M. Conger

 
/s/ Michael Comninos                        Director                            May 14, 1998
-----------------------------
Michael Comninos


/s/ Eduardo S. Elsztain                     Director                            May 14, 1998
------------------------------
Eduardo S. Elsztain


/s/ David Sean Hanna                        Director                            May 14, 1998
------------------------------
David Sean Hanna


/s/ Ove Hoegh                               Director                            May 14, 1998
-----------------------------
Ove Hoegh

</TABLE> 

                                       6
<PAGE>
<TABLE> 

<S>                                             <C>                            <C> 
 /s/ Keith R. Hulley                             Director                       May 14, 1998
-------------------------------
Keith R. Hulley


-------------------------------                  Director                       May __, 1998
Richard Katz


/s/ Paul Soros                                   Director                       May 14, 1998
--------------------------------
Paul Soros

</TABLE> 

                                       7
<PAGE>
 
                                    EXHIBITS

The following documents are filed as Exhibits hereto:

Exhibit No.                Description of Exhibits
-----------                -----------------------

 4.1      Apex Silver Mines Limited Employees' Share Option Plan*

 4.2      Apex Silver Mines Limited Non-Employee Directors' Share Option Plan*

 4.3      Form of Apex Silver Mines Limited Non-Qualified Stock Option Agreement

 5.1      Opinion of W. S. Walker & Company regarding the legality of the 
          Ordinary Shares being registered

23.1      Consent of W. S. Walker & Company (included as part of Exhibit 5.1)

23.2      Consent of Price Waterhouse LLP

24.1      Power of Attorney (included on the signature page of this 
          registration statement)

- - - - - - - - - - -

*incorporated by reference from Registrant's Form S-1 Registration Statement
 (file No. 333-34685), effective November 25, 1997.

                                       8
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 20493}]
{"company-data": {"conformed-name": "APEX SILVER MINES LTD", "cik": "0001011509", "assigned-sic": "1044", "irs-number": "000000000", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-53185", "film-number": "98629235"}, "business-address": {"street1": "CALEDONIAN HOUSE GROUND FL GEORGETOWN", "city": "GRAND CAYMAN CAYMAN", "state": "E9", "phone": "3499490050"}, "mail-address": {"street1": "CALEDONIAN HOUSE MARY STREET", "street2": "GEORGE TOWN GRAND CAYMAN ISLAND BWI"}}
As filed with the Securities and Exchange Commission on May 20, 1998
                                                          Registration No. 333-
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                                 --------------
                                    FORM S-8
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933
                                 --------------

                            APEX SILVER MINES LIMITED
               (Exact Name of Issuer as Specified in its Charter)

          Cayman Islands                                       Not Applicable
 (State or Other Jurisdiction of                               (I.R.S. Employer
 Incorporation or Organization)                              Identification No.)

                         Caledonian House, Ground Floor
                                   Mary Street
                            George Town, Grand Cayman
                       Cayman Islands, British West Indies
                                 (345) 949-0050
                    (Address of Principal Executive Offices)
                                 --------------

                            APEX SILVER MINES LIMITED
                          EMPLOYEES' SHARE OPTION PLAN

                            APEX SILVER MINES LIMITED
                             NON-EMPLOYEE DIRECTORS'
                                SHARE OPTION PLAN

                            APEX SILVER MINES LIMITED
                               NON-QUALIFIED STOCK
                                OPTION AGREEMENTS
                            (Full Title of the Plans)
                                 --------------

                                Thomas S. Kaplan
                             Chief Executive Officer
                          Apex Silver Mines Corporation
                         1700 Lincoln Street, Suite 3050
                             Denver, Colorado 80203
                                 (303) 839-5060
                     (Name and Address of Agent for Service)
   Telephone Number, Including Area Code, of Agent for Service: (303) 839-5060
CALCULATION OF REGISTRATION FEE
============================= ===================== ======================== ======================= ==========================
      Title of Shares              Amount to           Proposed Maximum         Proposed maximum             Amount of
      to be Registered          be Registered(1)      Offering Price Per       Aggregate Offering        Registration Fee
                                                             Share                  Price(2)
----------------------------- --------------------- ------------------------ ----------------------- --------------------------
Ordinary Shares (par value    3,040,625 Ordinary    Not Applicable           $33,212,744             $9,798
 $.01 per share)               Shares
============================= ===================== ======================== ======================= ==========================
(1)  There are also registered hereunder such additional indeterminate number of
     ordinary shares, par value $0.01 per share (the "Ordinary Shares"), as may
     be issued as a result of the antidilution provisions of the Apex Silver
     Mines Limited Employees' Share Option Plan (the "Employees' Share Option
     Plan"), the Apex Silver Mines Limited Non-Employee Directors' Share Option
     Plan (the "Non-Employee Directors' Share Option Plan") and the Apex Silver
     Mines Limited Non-Qualified Stock Option Agreements (the "Non-Qualified
     Stock Option Agreements").

(2)  Calculated on the basis of (i) 455,625 Ordinary Shares at $8.00 per
     Ordinary Share having an aggregate price of $3,645,000, pursuant to Rule
     457(h)(1) of the Securities Act of 1933, as amended (the "Act"), which is
     the aggregate offering price of certain of the Ordinary Shares subject to
     outstanding options under the Employees' Share Option Plan and all of the
     Non-Qualified Stock Option Agreements, (ii) 54,081 Ordinary Shares at $11
     3/16 per Ordinary Share having an aggregate price of $605,031, pursuant to
     Rule 457(h)(1) of the Act, which is the aggregate offering price of certain
     of the Ordinary Shares subject to outstanding options under the Employees'
     Share Option Plan and (iii) with respect to the remaining 2,530,919
     Ordinary Shares registered hereunder, using the average of the high and low
     prices reported on the American Stock Exchange on May 14, 1998, which is
     $11.44, having an aggregate offering price of $28,953,713, pursuant to Rule
     457(h)(1) and Rule 457(c) of the Act.

================================================================================
STATEMENT
                                   ---------

     This Registration Statement on Form S-8 is being filed with the Securities
and Exchange Commission (the "Commission") by Apex Silver Mines Limited, a
Cayman Islands Corporation (the "Company"), in order to register (i) 2,000,000
Ordinary Shares that will be available for issuance under the Employees' Share
Option Plan, (ii) 1,000,000 additional Ordinary Shares that will be available
for issuance under the Non-Employee Directors' Share Option Plan, all of which
may be issued upon the exercise of options granted under such plans, and (iii)
40,625 additional Ordinary Shares which may be issued by the Company pursuant to
the exercise of options granted in Non-Qualified Stock Option Agreements to each
of the seven non-employee directors of the Company.

                                       2
PART I

Item 1.  PLANS INFORMATION.

         Not included pursuant to Form S-8 instructions.

Item 2.  REGISTRANT INFORMATION AND PLANS ANNUAL INFORMATION.

         Not included pursuant to Form S-8 instructions.

                                    PART II

Item 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE.

     The Company hereby incorporates herein by reference the following
     documents:

     (1)  The description of the Company's Ordinary Shares contained in the
          Registration Statement on Form S-1 filed with the Securities and
          Exchange Commission (the "Commission") on August 29, 1997,
          Registration No. 333-34685, including amendments thereto and any
          report filed for the purpose of updating such description (the
          "Registration Statement");

     (2)  The Company's Annual Report on Form 10-K for the year ended December
          31, 1997, including portions of the Company's proxy statement dated
          April 15, 1998 relating to the Company's 1998 annual meeting of
          shareholders, which are incorporated therein by reference;

     (3)  The Company's proxy statement dated April 15, 1998;

     (4)  The Company's quarterly report on Form 10-Q for the quarter ended
          March 31, 1998; and

     (5)  All reports filed pursuant to Section 13(a) or 15(d) of the Securities
          Exchange Act of 1934, as amended (the "Exchange Act"), subsequent to
          the date of this filing.

     In addition, all documents filed by the Company pursuant to Sections 13(a),
13(c), 14 and 15(d) of the Exchange Act subsequent to the date of this
Registration Statement and prior to the filing of a post-effective amendment
which indicates that all securities offered herein have been sold or which
deregisters all securities then remaining unsold shall be deemed to be
incorporated herein by reference and to be a part hereof from the respective
date of filing of each such document.

Item 4.  DESCRIPTION OF SECURITIES.

         Not applicable.

Item 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL.

         Not applicable.

Item 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS.

     Cayman Islands law does not limit the extent to which a company's Articles
of Association may provide for the indemnification of officers and directors,
except to the extent that such provision may be held by the Cayman Islands
courts to be contrary to public policy (for instance, for purporting to provide
indemnification against the consequences of committing a crime). In addition, an
officer or director may not be indemnified for fraud or willful default.

                                       3
The Company's Articles contain provisions providing for the indemnity by
the Company of an officer, director, consultant, employee or agent of the
Company for threatened, pending or contemplated actions, suits or proceedings,
whether civil, criminal, administrative or investigative (including, without
limitation, an action by or the right of the company), brought against such
indemnified person by reason of the fact that such person was an officer,
director, consultant, employee or agent of the Company. In addition, the board
of directors may authorize the Company to purchase and maintain insurance on
behalf of any such person against any liability asserted against him and
incurred by him in any such capacity, or arising out of his status as such,
whether or not the company would have the power to indemnify him against such
liability under the provisions of the Articles.

     The Company also purchases directors and officers liability insurance from
third parties for its directors and officers. The Company's Article's provide
that directors and officers of the Company shall have no liability (i) for the
acts, receipts, neglects, defaults or omissions of any other such director or
officer or agent of the Company or (ii) by reason of his having joined in any
receipt for money not received by him personally or (iii) for any loss on
account of defect of title to any property of the Company or (iv) on account of
the insufficiency of any security in or upon which any money of the Company
shall be invested or (v) for any loss incurred through any bank, broker or other
agent or (vi) for any loss occasioned by any negligence, default, breach of
duty, breach of trust, error of judgment or oversight on his part of (vii) for
any loss, damage or misfortune whatsoever which may happen in or arise from the
execution or discharge of the duties, powers, authorities, or discretions of his
office or in relation thereto, unless the same shall happen through his own
dishonesty.

Item 7.  EXEMPTION FROM REGISTRATION CLAIMED.

         Not applicable.

Item 8.  EXHIBITS.

Exhibit No.     Description of Exhibits
----------      -----------------------

 4.1            Apex Silver Mines Limited Employees' Share Option Plan*

 4.2            Apex Silver Mines Limited Non-Employee Directors' Share Option
                Plan*

 4.3            Form of Apex Silver Mines Limited Non-Qualified Stock Option
                Agreement

 5.1            Opinion of W. S. Walker & Company regarding the legality of the
                Ordinary Shares being registered (Cayman Islands law)

23.1            Consent of W.S. Walker & Company (included as part of Exhibit
                5.1)

23.2            Consent of Price Waterhouse LLP

24.1            Power of Attorney (included on the signature page of this
                registration statement)

- - - - - - - - - - -

*incorporated by reference from Registrant's Form S-1 Registration Statement
 (file No. 333-34685), effective November 25, 1997.

Item 9.  UNDERTAKINGS

(a)      The undersigned hereby undertakes:

         (1)  to file, during any period in which offers or sales are being
              made, a post-effective amendment to this registration statement:

              (i)  to include any prospectus required by Section 10(a)(3) of the
                   Securities Act of 1933 (the "Securities Act");

                                       4
(ii)  to reflect in the prospectus any facts or events arising after
                the effective date of the registration statement (or the most
                recent post-effective amendment thereof) which, individually or
                in the aggregate, represent a fundamental change in the
                information set forth in the registration statement; and

          (iii) to include any material information with respect to the plan of
                distribution not previously disclosed in the registration
                statement or any material change to such information in the
                registration statement;

     provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) do not apply if
     the information to be included in a post-effective amendment by those
     paragraphs is contained in periodic reports filed by the registrant
     pursuant to Section 13 or Section 15(d) of the Exchange Act that are
     incorporated by reference in the registration statement.

     (2)  that, for the purpose of determining any liability under the
          Securities Act, each such post-effective amendment shall be deemed to
          be a new registration statement relating to the securities offered
          therein, and the offering of such securities at that time shall be
          deemed to be the initial bona fide offering thereof; and

     (3)  to remove from registration by means of a post-effective amendment any
          of the securities being registered which remain unsold at the
          termination of the offering.

(b)  The undersigned registrant hereby undertakes that, for purposes of
     determining any liability under the Securities Act, each filing of the
     registrant's Annual Report pursuant to Section 13(a) or Section 15(d) of
     the Exchange Act (and, where applicable, each filing of an employee benefit
     plan's Annual Report pursuant to Section 15(d) of the Exchange Act) that is
     incorporated by reference in the registration statement shall be deemed to
     be a new registration statement relating to the securities offered therein,
     and the offering of such securities at that time shall be deemed to be the
     initial bona fide offering thereof.

(c)  Insofar as indemnification for liabilities arising under the Securities Act
     may be permitted to directors, officers and controlling persons of the
     registrant pursuant to the foregoing provisions, or otherwise, the
     registrant has been advised that in the opinion of the Commission such
     indemnification is against public policy as expressed in the Act and is,
     therefore, unenforceable. In the event that a claim for indemnification
     against such liabilities (other than the payment by the registrant of
     expenses incurred or paid by a director, officer or controlling person of
     the registrant in the successful defense of any action, suit or proceeding)
     is asserted by such director, officer or controlling person in connection
     with the securities being registered, the registrant will, unless in the
     opinion of its counsel the matter has been settled by controlling
     precedent, submit to a court of appropriate jurisdiction the question
     whether such indemnification by it is against public policy as expressed in
     the Act and will be governed by the final adjudication of such issue.

                                       5
SIGNATURES

     Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this registration
statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in New York, New York, on this 14th day of May, 1998.

                                                 APEX SILVER MINES LIMITED

                                                 By: /s/ Thomas S. Kaplan
                                                    --------------------------

                                                 Name:  Thomas S. Kaplan
                                                 Title: Chairman of the Board

                                POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that each person whose signature appears
below constitutes and appoints Thomas S. Kaplan and Keith R. Hulley and each of
them severally, his true and lawful attorneys-in-fact and agents, with full
power of substitution and resubstitution, for him and in his name, place and
stead, in any and all capacities, to sign any and all amendments (including
post-effective amendments) to this registration statement, and to file the same,
with all exhibits thereto, and other documents in connection therewith, with the
Securities and Exchange Commission, granting unto said attorneys-in-fact and
agents, and each of them, full power and authority to do and perform each and
every act and thing requisite or necessary to be done in and about the premises,
as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents or either of
them, or their or his or her substitute or substitutes, may lawfully do or cause
to be done by virtue hereof.

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
Signature                                   Title                               Date
---------                                   -----                               ----

/s/ Thomas S. Kaplan                        Chairman of the Board               May 14, 1998
----------------------------  
Thomas S. Kaplan

/s/ Harry M. Conger                         Director                            May 14, 1998
-----------------------------
Harry M. Conger

 
/s/ Michael Comninos                        Director                            May 14, 1998
-----------------------------
Michael Comninos

/s/ Eduardo S. Elsztain                     Director                            May 14, 1998
------------------------------
Eduardo S. Elsztain

/s/ David Sean Hanna                        Director                            May 14, 1998
------------------------------
David Sean Hanna

/s/ Ove Hoegh                               Director                            May 14, 1998
-----------------------------
Ove Hoegh
6
/s/ Keith R. Hulley                             Director                       May 14, 1998
-------------------------------
Keith R. Hulley

-------------------------------                  Director                       May __, 1998
Richard Katz

/s/ Paul Soros                                   Director                       May 14, 1998
--------------------------------
Paul Soros
7
EXHIBITS

The following documents are filed as Exhibits hereto:

Exhibit No.                Description of Exhibits
-----------                -----------------------

 4.1      Apex Silver Mines Limited Employees' Share Option Plan*

 4.2      Apex Silver Mines Limited Non-Employee Directors' Share Option Plan*

 4.3      Form of Apex Silver Mines Limited Non-Qualified Stock Option Agreement

 5.1      Opinion of W. S. Walker & Company regarding the legality of the 
          Ordinary Shares being registered

23.1      Consent of W. S. Walker & Company (included as part of Exhibit 5.1)

23.2      Consent of Price Waterhouse LLP

24.1      Power of Attorney (included on the signature page of this 
          registration statement)

- - - - - - - - - - -

*incorporated by reference from Registrant's Form S-1 Registration Statement
 (file No. 333-34685), effective November 25, 1997.

                                       8