<PAGE>   1
                                                                EXHIBIT 10.60.2

                                                               [CONFORMED COPY]

                       AMENDMENT NO. 2 TO CREDIT AGREEMENT


         AMENDMENT dated as of December 31, 1999 to the Credit Agreement dated
as of September 8, 1999 (as amended, the "CREDIT AGREEMENT") among WILLIAMS
COMMUNICATIONS, INC. (the "BORROWER"), WILLIAMS COMMUNICATIONS GROUP, INC., as
Guarantor, the LENDERS party thereto (the "LENDERS") and BANK OF AMERICA, N.A.,
as Administrative Agent (the "ADMINISTRATIVE AGENT"), THE CHASE MANHATTAN BANK,
as Syndication Agent, and BANK OF MONTREAL and THE BANK OF NEW YORK, as
Co-Documentation Agents.

                                  WITNESSETH:

         WHEREAS, the parties hereto have entered into the Credit Agreement and
now desire to make certain amendments to the Credit Agreement as set forth
herein;

         NOW, THEREFORE, the parties hereto agree as follows:

         SECTION 1. Defined Terms; References. Unless otherwise specifically
defined herein, each term used herein which is defined in the Credit Agreement
has the meaning assigned to such term in the Credit Agreement. Each reference to
"hereof", "hereunder", "herein" and "hereby" and each other similar reference
and each reference to "this Agreement" and each other similar reference
contained in the Credit Agreement shall, after this Amendment becomes effective,
refer to the Credit Agreement as amended hereby.

         SECTION 2. Additional Definitions. (a) Section 1.01(a) of the Credit
Agreement is hereby amended by inserting the following new defined terms in
appropriate alphabetical order:

                  "Permitted Specified Security Hedging Transactions" means
         options, collars, forwards and other similar transactions with respect
         to any Specified Security entered into by the Borrower or any of its
         Subsidiaries to hedge against changes in the market price of such
         Specified Security.

                  "Specified Security" means publicly traded equity securities
         of actual or prospective customers or vendors of the Borrower and its
         Subsidiaries acquired by the Borrower and its Subsidiaries in
         connection with (or pursuant to warrants, options or rights acquired in
         connection with) commercial agreements with such customers or vendors;
         provided

<PAGE>   2


         that securities of the Borrower or any of its Subsidiaries or
         Affiliates shall not constitute Specified Securities.

         SECTION 3. Indebtedness; Certain Equity Securities. (a) Section 6.01 of
the Credit Agreement is hereby amended by inserting, immediately following
clause (p) thereof, new clause (q) to read in its entirety as follows:

                  "(q) Permitted Specified Security Hedging Transactions;"

         SECTION 4. Liens. Section 6.02(a) of the Credit Agreement is hereby
amended by (i) deleting the word "and" at the end of clause (vii) thereof, (ii)
redesignating clause (viii) thereof as clause (ix) and (iii) inserting,
immediately following clause (vii), a new clause (viii) to read in its entirety
as follows:

                  "(viii) Liens on a Specified Security securing Permitted
         Specified Security Hedging Transactions with respect to such Specified
         Security; and"

         SECTION 5. Fundamental Changes. Section 6.03(c) of the Credit Agreement
is hereby amended by (i) adding, following the parenthetical expression "(a
"Trading Subsidiary")" on the seventh line thereof, the expression "and (vi) the
holding of Qualifying Borrower Indebtedness permitted under Section 6.01(q)" and
(ii) adding, following the expression "Qualifying Equity Interests in the
Borrower" on the ninth line thereof, the expression "Qualifying Borrower
Indebtedness,".

         SECTION 6. Investments. (a) Section 6.04 of the Credit Agreement is
hereby amended by (i) deleting the word "and" at the end of clause (p) thereof
immediately following the words "Qualifying Equity Interests in Holdings;" (ii)
redesignating clause (q) as clause (r), and (iii) inserting a new clause (q) to
read in its entirety as follows:

                  "(q) Investments made in any Person (a "REINVESTMENT PERSON")
         in whom the Borrower or any of its Subsidiaries has, or at any time
         after the Closing Date had, an Investment permitted under clause (b),
         (f) or (p) above or this clause (q) (an "ORIGINAL INVESTMENT");
         provided that the aggregate amount of Investments in any Reinvestment
         Person permitted under this clause (q) may not exceed the aggregate
         amount of the cash proceeds received, within 270 days prior to the
         making of such Investment, by the Borrower and its Subsidiaries from
         sales or other dispositions of, or distributions with respect to,
         Original Investments in such Reinvestment Person; and"

                                       2
<PAGE>   3


          (b) The proviso to Section 6.04 of the Credit Agreement is hereby
amended and restated in its entirety as follows:

                  "provided that the aggregate amount of all Investments (valued
         at the cost of acquisition thereof, without regard to any increase or
         decrease in the value thereof based on subsequent performance of the
         Person in which such Investment is held), but net, in case of each such
         Investment (but not below zero), of any distributions received by the
         Borrower or any Subsidiary Loan Party in respect of such Investment and
         any proceeds received upon any disposition (other than a disposition to
         Holdings or any of its Subsidiaries or the Parent or any of its
         Subsidiaries) of such Investment, made pursuant to Sections 6.04(j) and
         6.04(k) on or prior to any date, or referred to in Section 6.04(c)(i),
         the proviso to Section 6.04(d) and Section 6.04(e)(ii) and made on or
         prior to such date, shall not exceed the sum of (i) $275,000,000 plus
         (ii) an amount (which amount, for purposes of this proviso only, shall
         not be less than zero) equal to (x) the amount of Additional Capital as
         of such date minus (y) (A) payments of principal of the Intercompany
         Note made pursuant to Section 6.07(b)(ii)(x) on or prior to such date,
         (B) acquisitions of ADP Property permitted under Section 6.04(g) made
         on or prior to such date and (C) Capital Expenditures permitted under
         Section 6.08(b) made on or prior to such date."

         (c) Schedule 6.04 to the Credit Agreement is hereby amended by
inserting the following new paragraph 13 at the end thereof:

                  "ChoiceSeat - WCG owns 1,180,667 shares of Series A Preferred
         Stock and 5,572,333 shares of common stock of CSI, Incorporated, for a
         total investment of about $27,000,000."

         SECTION 7. Asset Sales. Section 6.05(a) of the Credit Agreement is
hereby amended by (i) inserting the phrase "sales of inventory" immediately
following the word "capacity," and (ii) inserting the phrase ", in each case"
immediately following the phrase "Cash Equivalent Investments".

         SECTION 8. Amendment to Financial Covenants. (a) The table set forth in
Section 6.08 of the Credit Agreement is hereby amended to read in its entirety
as follows:

                                       3
<PAGE>   4

<TABLE>
<CAPTION>
                             "Fiscal Year                Amount
                             ------------                ------
<S>                                                <C>
                                1999               $   2,500,000,000

                                2000               $   2,200,000,000

                                2001               $   1,500,000,000

                                2002               $     700,000,000

                                2003               $     700,000,000

                                2004               $     700,000,000

                                2005               $     700,000,000

                                2006               $     700,000,000"
</TABLE>

         (b) The table set forth in Section 6.16 of the Credit Agreement is
hereby amended to read in its entirety as follows:

<TABLE>
<CAPTION>
                              "Period                   Amount
                              -------                   ------
<S>                                                <C>
                    October 1, 1999-              $             0
                    December 31, 1999

                    January 1, 2000-              $             0
                    March 31,2000

                    April 1, 2000-                $             0
                    June 30, 2000

                    July 1, 2000-                 $    80,000,000
                    September 30, 2000

                    October 1, 2000-              $   200,000,000
                    December 31, 2000

                    January 1, 2001-              $   225,000,000
                    March 31, 2001

                    April 1, 2001-                $   325,000,000"
                    June 30, 2001
</TABLE>

         (c) The table set forth in Section 6.17(a) of the Credit Agreement is
hereby amended to read in its entirety as follows:

                                       4
<PAGE>   5

<TABLE>
<CAPTION>
                             "Period                   Total Leverage Ratio
                             -------                   --------------------
<S>                                                         <C>
                        December 31, 2000-                  15.00:1.00
                        June 29, 2001

                        June 30, 2001-                      12.00:1.00
                        December 30, 2001

                        December 31, 2001-                  11.00:1.00
                        June 29, 2002

                        June 30, 2002-                      9.00:1.00
                        December 30, 2002

                        December 31, 2002-                  7.00:1.00
                        December 30, 2003

                        December 31, 2003-                  4.00:1.00"
                        and thereafter
</TABLE>

         (d) The table set forth in Section 6.18 of the Credit Agreement is
hereby amended to read in its entirety as follows:

<TABLE>
<CAPTION>
                             "Period                  Senior Leverage Ratio
                             -------                  ---------------------
<S>                                                         <C>
                        December 31, 2000-                  9.00:1.00
                        June 29, 2001

                        June 30, 2001-                      7.00:1.00
                        December 30, 2001

                        December 31, 2001-                  5.25:1.00
                        December 30, 2002

                        December 31, 2002-                  3.25:1.0
                        December 30, 2003

                        December 31, 2003-                  2.50:1.00"
                        and thereafter
</TABLE>

         (e) In the table set forth in Section 6.19 of the Credit Agreement is
hereby amended to read in its entirety as follows:

<TABLE>
<CAPTION>
                                "Period                 Interest Coverage Ratio
                                -------                 -----------------------
<S>                                                            <C>
                        July 1, 2001-                         1.00:1.00
                        December 31, 2001

                        January 1, 2002-                      1.25:1.00
                        December 31, 2002

                        January 1, 2003-                      2.25:1.00
                        December 31, 2003

                        January 1, 2004-                      3.00:1.00"
                        and thereafter
</TABLE>

                                       5
<PAGE>   6


         SECTION 9. Representations of Borrower. The Borrower represents and
warrants that, as of the Amendment Effective Date, both before and after giving
effect to this Amendment, (i) the representations and warranties of the Borrower
set forth in Article 3 of the Credit Agreement are true and correct and (ii) no
Default has occurred and is continuing.

         SECTION 10. Amendment Fee. On or prior to the seventh Business Day
following the Signature Receipt Date, the Borrower shall pay the Administrative
Agent, for the ratable accounts of the Lenders who shall have executed and
delivered a counterpart hereof (or other written confirmation in form
satisfactory to the Administrative Agent that such Lender has signed a
counterpart hereof) to the Administrative Agent on or prior to March 30, 2000,
an amendment fee in an amount equal to 0.075% of the aggregate Commitments of
such Lenders.

         SECTION 11. Governing Law. This Amendment shall be governed by and
construed in accordance with the laws of the State of New York.

         SECTION 12. Counterparts. This Amendment may be signed in any number of
counterparts, each of which shall be an original, with the same effect as if the
signatures thereto and hereto were upon the same instrument.

         SECTION 13. Effectiveness. This Amendment shall become effective on and
as of the date hereof (the "AMENDMENT EFFECTIVE DATE") on the date that the
Administrative Agent shall have received (the "SIGNATURE RECEIPT DATE") from
each of the Loan Parties and the Required Lenders a counterpart hereof signed by
such party or facsimile or other written confirmation (in form satisfactory to
the Administrative Agent) that such party has signed a counterpart hereof.

                                       6
<PAGE>   7


         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed as of the date first above written.

                                      WILLIAMS COMMUNICATIONS, INC.

                                      By:    /s/ Howard Kalika
                                             -----------------------------------
                                             Title: Vice President and Treasurer

                                      WILLIAMS COMMUNICATIONS GROUP, INC.

                                      By:    /s/ Howard Kalika
                                            ------------------------------------
                                            Title: Vice President and Treasurer

                                      BANK OF AMERICA, N.A.

                                      By:    /s/ Roselyn Drake
                                            ------------------------------------
                                            Title: Managing Director

                                      THE CHASE MANHATTAN BANK

                                      By:    /s/ Constance M. Coleman
                                            ------------------------------------
                                            Title: Vice President

                                      BANK OF MONTREAL

                                      By:    /s/ Sarah Kim
                                            ------------------------------------
                                            Title: Director


<PAGE>   8


                                      THE BANK OF NEW YORK

                                      By:    /s/ Brendan Nedzi
                                             -----------------------------------
                                             Title: Senior Vice President

                                      SCOTIABANC INC.

                                      By:    /s/ W.J. Brown
                                             -----------------------------------
                                             Title: Managing Director

                                      ABN AMRO BANK N.V.

                                      By:    /s/ Ann Schwalbenberg
                                             -----------------------------------
                                             Title: Vice President

                                      By:    /s/ Ravneet Mumick
                                             -----------------------------------
                                             Title: Vice President

                                      FLEET NATIONAL BANK

                                      By:
                                             -----------------------------------
                                             Title:

                                      CIBC INC.

                                      By:    /s/ Michele E. Roller
                                             -----------------------------------
                                             Title: Executive Director
                                                    CIBC World Markets Corp.
                                                    as Agent


<PAGE>   9


                                      CREDIT SUISSE FIRST BOSTON

                                      By:    /s/ Joel Glodowski
                                            ------------------------------------
                                            Title: Managing Director

                                      By:    /s/ Chris T. Horgan
                                            ------------------------------------
                                            Title: Vice President

                                      DEUTSCHE BANK AG
                                      NEW YORK AND/OR CAYMAN ISLAND
                                      BRANCH

                                      By:    /s/ Jon D. Storck
                                            ------------------------------------
                                            Title: Vice President

                                      By:    /s/ Sangita Gupte
                                            ------------------------------------
                                            Title: Associate

                                      CREDIT LYONNAIS NEW YORK BRANCH

                                      By:
                                            ------------------------------------
                                            Title:


<PAGE>   10


                                      BANK AUSTRIA CREDITANSTALT
                                      CORPORATE FINANCE, INC.

                                      By: /s/ Richard Varalla
                                         ---------------------------------------
                                         Title: Senior Associate

                                      By: /s/ William E. McCollum, Jr.
                                         ---------------------------------------
                                         Title: Vice President

                                      FIRST UNION NATIONAL BANK

                                      By: /s/ Steven J. Haas
                                         ---------------------------------------
                                         Title: Senior Vice President

                                      IBM CREDIT CORPORATION

                                      By: /s/ Ronald J. Bachner
                                         ---------------------------------------
                                         Title: Manager Commercial and Specialty
                                             Financing

                                      THE INDUSTRIAL BANK OF JAPAN,
                                      LIMITED, NEW YORK BRANCH

                                      By: /s/ Ryusuke Aya
                                         ---------------------------------------
                                         Title: Senior Vice President, Houston
                                                         Office


<PAGE>   11


                                      BANK OF OKLAHOMA N.A.

                                      By: /s/ Robert D. Mattax
                                         ---------------------------------------
                                         Title: Senior Vice President

                                      THE FIRST NATIONAL BANK OF
                                              CHICAGO

                                      By:
                                         ---------------------------------------
                                         Title:

                                      KBC BANK, N.V.

                                      By: /s/ Robert Snauffer
                                         ---------------------------------------
                                         Title: First Vice President

                                      By: /s/ Patrick A. Janssens
                                         ---------------------------------------
                                         Title: Vice President

                                      THE FUJI BANK, LIMITED

                                      By: /s/ Jacques Azagury
                                         ---------------------------------------
                                         Title: Senior Vice President & Manager


<PAGE>   12


Acknowledged and agreed:

CNG COMPUTER NETWORKING GROUP, INC.
CRITICAL CONNECTIONS, INC.
DATA COMMUNICATIONS 2000, INC.
INTERNET ENGINEERING & CONSULTANT, INC.
WCS COMMUNICATIONS SYSTEMS,
     INC.
WCS MICROWAVE SERVICES, INC.
WCS, INC.
WILLIAMS COMMUNICATIONS OF
     VIRGINIA, INC.
WILLIAMS GLOBAL COMMUNICATIONS
     HOLDINGS, INC.
WILLIAMS INTERNATIONAL
     VENTURES COMPANY
WILLIAMS LEARNING NETWORK,
     INC.
WILLIAMS LOCAL NETWORK, INC.
WILLIAMS WIRELESS, INC.


All By: /s/ Howard Kalika
        -----------------------------------
        Title: Vice President and Treasurer




THE WILLIAMS COMPANIES, INC.


By:    /s/ John Bumgarner
       -------------------------------------
       Title: Senior Vice President