FORM 8-K


                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


                                 CURRENT REPORT

                       Pursuant to Section 13 or 15(d) of
                       The Securities Exchange Act of 1934


 Date of Report (Date of earliest event reported):     September 8, 1998
                                                  -----------------------------


                           AERIAL COMMUNICATIONS, INC.
              ----------------------------------------------------
             (Exact name of registrant as specified in its charter)


        Delaware                    0-28262                 39-1706857
----------------------------      ------------          ------------------
(State or other jurisdiction      (Commission            (IRS Employer
     of incorporation)             File Number)         Identification No.)



8410 West Bryn Mawr Avenue, Chicago, Illinois               60631
---------------------------------------------             ----------
  (Address of principal executive offices)                (Zip Code)


Registrant's telephone number, including area code: (773) 399-4200


                                 Not Applicable
          ------------------------------------------------------------
          (Former name or former address, if changed since last report)



<PAGE>



Item 5.           Other Events.
                  ------------

                  Pursuant  to a  Purchase  Agreement  dated  June 1,  1998 (the
"Purchase Agreement") by and among Aerial Communications,  Inc. (the "Company"),
Aerial Operating Co., Inc., a wholly-owned  subsidiary of the Company  (formerly
known as APT Operating Company, Inc.) ("AOC"), Telephone and Data Systems, Inc.,
the parent  corporation  of the  Company  ("TDS"),  and Sonera  Ltd.,  a limited
liability  company organized under the laws of Finland (formerly known as Sonera
Corporation)  ("Sonera"),  on  September  8,  1998,  Sonera  purchased  from AOC
2,410,482  shares  of  common  stock  of AOC  (the  "Purchased  Shares")  for an
aggregate purchase price of $200 million, representing a 19.423% equity interest
in AOC. Sonera will have the right under certain  circumstances to exchange each
Purchased Share for 6.72919 Common Shares of Aerial  ("Aerial  Common  Shares"),
subject to adjustment.  Upon the exchange of all of the Purchased Shares at such
exchange rate,  Sonera would own  approximately  an 18.5% equity interest in the
Company,  reflecting a purchase  price  equivalent to  approximately  $12.33 per
Aerial  Common  Share.  The number of Purchased  Shares is subject to adjustment
depending on the future performance of the market price of Aerial Common Shares.
Depending on the stock price, the price paid will range from a low of $12.33 per
equivalent  Aerial share to a high of $16.68 per equivalent Aerial Common Share,
which would represent approximately a 14.3% equity interest in the Company.

                  In connection with the closing of the Purchase Agreement,  the
parties entered into the following  agreements:  (i) an Investment  Agreement by
and between TDS, Aerial, AOC and Sonera, (ii) a Registration Rights Agreement by
and between  Aerial and Sonera,  (iii) a Joint Venture  Agreement by and between
Aerial,  AOC and Sonera  Corporation U.S., and (iv) a Supplemental  Agreement by
and between  Aerial,  AOC and Sonera.  Copies of such  agreements  are  attached
hereto as exhibits and incorporated herein by reference.

                  In addition,  pursuant to the terms of the Purchase Agreement,
at the closing,  (i) a Revolving  Credit  Agreement dated August 1, 1995 between
TDS and Aerial,  pursuant to which  Aerial was  indebted to TDS in the amount of
$665 million, plus accrued interest, was terminated,  and a new Revolving Credit
Agreement between TDS and AOC was substituted, pursuant to which AOC is indebted
to TDS in the same amount,  (ii) Aerial executed a Guaranty of AOC's obligations
to TDS under the new Revolving  Credit  Agreement,  and (iii) the Tax Allocation
Agreement  dated January 1, 1996 between TDS and Aerial was amended and restated
in order to  include  AOC as a party.  Copies of such  agreements  are  attached
hereto as exhibits and incorporated herein by reference.

                  There were no prior material relationships between the Company
or any of the Company's  affiliates,  any director or officer of the Company, or
any  associate of any such director or officer,  on the one hand,  and Sonera on
the other hand.

                  Additional   information   concerning   this   transaction  is
contained in the Purchase  Agreement  which was filed with the Commission by the
Company on Form 8-K on June 16, 1998, and is incorporated herein by reference.

                                      - 1 -

<PAGE>



                                   SIGNATURES


         Pursuant to the  requirements  of the Securities  Exchange Act of 1934,
the  registrant  has duly  caused  this report to be signed on its behalf by the
undersigned, thereto duly authorized.


                               AERIAL COMMUNICATIONS, INC.
                               (Registrant)


Date:  September 17, 1998     By:   /s/ J. Clarke Smith
                                    --------------------------------------
                                    J. Clarke Smith
                                    Vice President - Finance and Administration,
                                    Chief Financial Officer and Treasurer

















































            SIGNATURE PAGE TO AERIAL FORM 8-K DATED SEPTEMBER 8, 1998



                                      - 2 -

<PAGE>



                                  EXHIBIT INDEX


         Exhibit Number                              Description of Exhibit
         --------------                              ----------------------

             99.1                                    Aerial news  release  dated
                                                     September 8, 1998

             99.2                                    The  Investment   Agreement
                                                     between  Telephone and Data
                                                     Systems,    Inc.,    Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Ltd.    (formerly    Sonera
                                                     Corporation),         dated
                                                     September 8, 1998.

             99.3                                    The   Registration   Rights
                                                     Agreement   between  Aerial
                                                     Communications,   Inc.  and
                                                     Sonera    Ltd.    (formerly
                                                     Sonera Corporation),  dated
                                                     September 8, 1998.

             99.4                                    The Joint Venture Agreement
                                                     between              Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Corporation   U.S.,   dated
                                                     September 8, 1998.

             99.5                                    The Supplemental  Agreement
                                                     between              Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Ltd.    (formerly    Sonera
                                                     Corporation),         dated
                                                     September 8, 1998.

             99.6                                    The     Tax      Allocation
                                                     Agreement between Telephone
                                                     and  Data  Systems,   Inc.,
                                                     Aerial Communications, Inc.
                                                     and Aerial  Operating  Co.,
                                                     Inc.      (formerly     APT
                                                     Operating  Company,  Inc.),
                                                     dated September 8, 1998.

             99.7                                    The    Guaranty     between
                                                     Telephone and Data Systems,
                                                     Inc.       and       Aerial
                                                     Communications, Inc., dated
                                                     August 31, 1998.

             99.8                                    The    Revolving     Credit
                                                     Agreement between Telephone
                                                     and Data Systems,  Inc. and
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,    Inc.),    dated
                                                     August 31, 1998.


                                      - 3 -

<PAGE>



             99.9                                    The   Purchase    Agreement
                                                     between  Telephone and Data
                                                     Systems,    Inc.,    Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Ltd.    (formerly    Sonera
                                                     Corporation), dated June 1,
                                                     1998,       is       hereby
                                                     incorporated  by  reference
                                                     to  Exhibit   99.2  to  the
                                                     Company's  Form  8-K  dated
                                                     June 1, 1998.

























                                      - 4 -

<PAGE>
[{"type": "8-K", "sequence": "1", "description": "FORM 8-K", "secsgml_size_bytes": 11618}]
{"company-data": {"conformed-name": "AERIAL COMMUNICATIONS INC", "cik": "0001008614", "assigned-sic": "4812", "irs-number": "391706857", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "8-K", "act": "34", "file-number": "000-28262", "film-number": "98711096"}, "business-address": {"street1": "8410 WEST BRYN MAWR AVE", "street2": "STE 1100", "city": "CHICAGO", "state": "IL", "zip": "60631", "phone": "3123994200"}, "mail-address": {"street1": "8410 WEST BRYN MAWR AVE", "street2": "STE 1100", "city": "CHICAGO", "state": "IL", "zip": "60631-3486"}, "former-company": {"former-conformed-name": "AMERICAN PORTABLE TELECOM INC", "date-changed": "19960221"}}
FORM 8-K

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                 CURRENT REPORT

                       Pursuant to Section 13 or 15(d) of
                       The Securities Exchange Act of 1934

 Date of Report (Date of earliest event reported):     September 8, 1998
                                                  -----------------------------

                           AERIAL COMMUNICATIONS, INC.
              ----------------------------------------------------
             (Exact name of registrant as specified in its charter)

        Delaware                    0-28262                 39-1706857
----------------------------      ------------          ------------------
(State or other jurisdiction      (Commission            (IRS Employer
     of incorporation)             File Number)         Identification No.)

8410 West Bryn Mawr Avenue, Chicago, Illinois               60631
---------------------------------------------             ----------
  (Address of principal executive offices)                (Zip Code)

Registrant's telephone number, including area code: (773) 399-4200

                                 Not Applicable
          ------------------------------------------------------------
          (Former name or former address, if changed since last report)
Item 5.           Other Events.
                  ------------

                  Pursuant  to a  Purchase  Agreement  dated  June 1,  1998 (the
"Purchase Agreement") by and among Aerial Communications,  Inc. (the "Company"),
Aerial Operating Co., Inc., a wholly-owned  subsidiary of the Company  (formerly
known as APT Operating Company, Inc.) ("AOC"), Telephone and Data Systems, Inc.,
the parent  corporation  of the  Company  ("TDS"),  and Sonera  Ltd.,  a limited
liability  company organized under the laws of Finland (formerly known as Sonera
Corporation)  ("Sonera"),  on  September  8,  1998,  Sonera  purchased  from AOC
2,410,482  shares  of  common  stock  of AOC  (the  "Purchased  Shares")  for an
aggregate purchase price of $200 million, representing a 19.423% equity interest
in AOC. Sonera will have the right under certain  circumstances to exchange each
Purchased Share for 6.72919 Common Shares of Aerial  ("Aerial  Common  Shares"),
subject to adjustment.  Upon the exchange of all of the Purchased Shares at such
exchange rate,  Sonera would own  approximately  an 18.5% equity interest in the
Company,  reflecting a purchase  price  equivalent to  approximately  $12.33 per
Aerial  Common  Share.  The number of Purchased  Shares is subject to adjustment
depending on the future performance of the market price of Aerial Common Shares.
Depending on the stock price, the price paid will range from a low of $12.33 per
equivalent  Aerial share to a high of $16.68 per equivalent Aerial Common Share,
which would represent approximately a 14.3% equity interest in the Company.

                  In connection with the closing of the Purchase Agreement,  the
parties entered into the following  agreements:  (i) an Investment  Agreement by
and between TDS, Aerial, AOC and Sonera, (ii) a Registration Rights Agreement by
and between  Aerial and Sonera,  (iii) a Joint Venture  Agreement by and between
Aerial,  AOC and Sonera  Corporation U.S., and (iv) a Supplemental  Agreement by
and between  Aerial,  AOC and Sonera.  Copies of such  agreements  are  attached
hereto as exhibits and incorporated herein by reference.

                  In addition,  pursuant to the terms of the Purchase Agreement,
at the closing,  (i) a Revolving  Credit  Agreement dated August 1, 1995 between
TDS and Aerial,  pursuant to which  Aerial was  indebted to TDS in the amount of
$665 million, plus accrued interest, was terminated,  and a new Revolving Credit
Agreement between TDS and AOC was substituted, pursuant to which AOC is indebted
to TDS in the same amount,  (ii) Aerial executed a Guaranty of AOC's obligations
to TDS under the new Revolving  Credit  Agreement,  and (iii) the Tax Allocation
Agreement  dated January 1, 1996 between TDS and Aerial was amended and restated
in order to  include  AOC as a party.  Copies of such  agreements  are  attached
hereto as exhibits and incorporated herein by reference.

                  There were no prior material relationships between the Company
or any of the Company's  affiliates,  any director or officer of the Company, or
any  associate of any such director or officer,  on the one hand,  and Sonera on
the other hand.

                  Additional   information   concerning   this   transaction  is
contained in the Purchase  Agreement  which was filed with the Commission by the
Company on Form 8-K on June 16, 1998, and is incorporated herein by reference.

                                      - 1 -
SIGNATURES

         Pursuant to the  requirements  of the Securities  Exchange Act of 1934,
the  registrant  has duly  caused  this report to be signed on its behalf by the
undersigned, thereto duly authorized.

                               AERIAL COMMUNICATIONS, INC.
                               (Registrant)

Date:  September 17, 1998     By:   /s/ J. Clarke Smith
                                    --------------------------------------
                                    J. Clarke Smith
                                    Vice President - Finance and Administration,
                                    Chief Financial Officer and Treasurer

            SIGNATURE PAGE TO AERIAL FORM 8-K DATED SEPTEMBER 8, 1998

                                      - 2 -
EXHIBIT INDEX

         Exhibit Number                              Description of Exhibit
         --------------                              ----------------------

             99.1                                    Aerial news  release  dated
                                                     September 8, 1998

             99.2                                    The  Investment   Agreement
                                                     between  Telephone and Data
                                                     Systems,    Inc.,    Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Ltd.    (formerly    Sonera
                                                     Corporation),         dated
                                                     September 8, 1998.

             99.3                                    The   Registration   Rights
                                                     Agreement   between  Aerial
                                                     Communications,   Inc.  and
                                                     Sonera    Ltd.    (formerly
                                                     Sonera Corporation),  dated
                                                     September 8, 1998.

             99.4                                    The Joint Venture Agreement
                                                     between              Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Corporation   U.S.,   dated
                                                     September 8, 1998.

             99.5                                    The Supplemental  Agreement
                                                     between              Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Ltd.    (formerly    Sonera
                                                     Corporation),         dated
                                                     September 8, 1998.

             99.6                                    The     Tax      Allocation
                                                     Agreement between Telephone
                                                     and  Data  Systems,   Inc.,
                                                     Aerial Communications, Inc.
                                                     and Aerial  Operating  Co.,
                                                     Inc.      (formerly     APT
                                                     Operating  Company,  Inc.),
                                                     dated September 8, 1998.

             99.7                                    The    Guaranty     between
                                                     Telephone and Data Systems,
                                                     Inc.       and       Aerial
                                                     Communications, Inc., dated
                                                     August 31, 1998.

             99.8                                    The    Revolving     Credit
                                                     Agreement between Telephone
                                                     and Data Systems,  Inc. and
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,    Inc.),    dated
                                                     August 31, 1998.

                                      - 3 -
99.9                                    The   Purchase    Agreement
                                                     between  Telephone and Data
                                                     Systems,    Inc.,    Aerial
                                                     Communications,       Inc.,
                                                     Aerial  Operating Co., Inc.
                                                     (formerly   APT   Operating
                                                     Company,  Inc.) and  Sonera
                                                     Ltd.    (formerly    Sonera
                                                     Corporation), dated June 1,
                                                     1998,       is       hereby
                                                     incorporated  by  reference
                                                     to  Exhibit   99.2  to  the
                                                     Company's  Form  8-K  dated
                                                     June 1, 1998.

                                      - 4 -