<PAGE>

                                                                    EXHIBIT 10.2


                                                                  EXECUTION COPY

                           THIRD AMENDMENT AND WAIVER

     THIRD AMENDMENT AND WAIVER, dated as of September 15, 2000 (the "Third
                                                                      -----
Amendment"), to the Credit Agreement, dated as of July 22, 1999 (as amended,
---------
supplemented or otherwise modified, the "Credit Agreement"), among BANCTEC,
                                         ----------------
INC., a Delaware corporation (the "Borrower"), the several banks and other
                                   --------
financial institutions or entities from time to time parties thereto (the
"Lenders"), ABN AMRO Bank N.V., as Co-Agent, THE CHASE MANHATTAN BANK (formerly,
--------
CHASE BANK OF TEXAS, N.A.) ("CHASE"), as syndication agent (in such capacity,
                             -----
the "Syndication Agent"), and THE CHASE MANHATTAN BANK (formerly, CHASE BANK OF
     -----------------
TEXAS, N.A.), as administrative agent (in such capacity, the "Administrative
                                                              --------------
Agent").
-----

                             W I T N E S S E T H:
                             --------------------

     WHEREAS, the Borrower, the Lenders, the Administrative Agent and the
Syndication Agent are parties to the Credit Agreement;

     WHEREAS, the Borrower has requested (i) waiver of certain provisions of the
Credit Agreement and (ii) certain amendments to the Credit Agreement as set
forth herein; and

     WHEREAS, Welsh, Carson, Anderson & Stowe, VIII, L.P., (the "Sponsor")
                                                                 -------
shall guarantee at least $35,000,000 of the Loans made by the Lenders (pro rata
                                                                       --- ----
based on each Lender's percentage share of the outstanding Loans) through the
execution of an amendment and restatement (as further defined below, the
"Sponsor Guarantee"), substantially in the form of Exhibit A hereto, of the
------------------
Guarantee, dated as of May 25, 2000, made by the Sponsor and the delivery of a
letter of credit (the "Sponsor Letter of Credit") in the name of the
                       ------------------------
Administrative Agent for the benefit of the Lenders substantially in the form of
Exhibit B hereto;

     WHEREAS, the Borrower shall receive at least $15,000,000 in proceeds from
the issuance of preferred stock to the Sponsor; and

     WHEREAS, the Required Lenders have consented to the requested waivers and
amendments as set forth herein;

     NOW THEREFORE, in consideration of the premises and the mutual covenants
hereinafter set forth, the parties hereto hereby agree as follows:

     1.  Definitions. Terms defined in the Credit Agreement are used herein
         -----------
with the respective meanings given to them therein.

     2.  Amendments to Section 1 of the Credit Agreement.
         -----------------------------------------------

         (a)  Subsection 1.1 of the Credit Agreement is hereby amended by (i)
     deleting in its entirety the definition of Loan Documents and (ii)
     inserting the following new definitions in alphabetical order:
<PAGE>

                                                                               2



          "Loan Documents":  This Agreement, the Security Documents, the Notes,
           --------------
if any, and, on and after the Third Amendment Effective Date, the Sponsor
Guarantee and the Sponsor Letter of Credit.

          "Sponsor Guarantee":  The Amended and Restated Guarantee, dated as of
           -----------------
September 15, 2000, by the Sponsor in favor of the Administrative Agent on
behalf of the Lenders.

          "Sponsor Letter of Credit":  as defined in the Third Amendment.
           ------------------------

          "Third Amendment":  The Third Amendment and Waiver, dated as of
           ---------------
September 15, 2000, to this Agreement.

          "Third Amendment Effective Date":  as defined in the Third Amendment.
           ------------------------------

          (b)  The definition of "Consolidated EBITDA" is hereby amended by
deleting the last sentence at the end thereof and inserting in lieu thereof
the following sentence:

          "Notwithstanding anything herein to the contrary, for the quarters
     ended September 30, 2000 and December 31, 2000, for purposes of calculating
     Consolidated EBITDA, (a) GAAP shall be determined without regard to Staff
     Accounting Bulletin No. 101, "Revenue Recognition," (b) any extraordinary
     or non-recurring cash charges may be added to Consolidated Net Income in
     determining Consolidated EBITDA and (c) to the extent that Consolidated
     EBITDA is less than as is required by the covenant set forth in Subsection
     7.1 (e), Consolidated EBITDA shall include the cash investment (through the
     purchase of preferred or common stock or Indebtedness of the Borrower, in
     each case on terms subordinating such investment to Indebtedness of the
     Borrower to the Lenders at least to the same extent as the Sponsor Notes,
     or otherwise on terms and conditions satisfactory to the Administrative
     Agent) in the Borrower made by the Sponsor in order to insure the
     Borrower's compliance with such covenant."

         (c)  The definition of "Revolving Commitment" is hereby amended by
inserting at the end thereof the following sentence:

         "Notwithstanding anything herein to the contrary, on and after the
     Third Amendment Effective Date, the Total Revolving Commitments shall be
     reduced to the aggregate amount of $43,569,420.00, the then outstanding
     Revolving Extensions of Credit."

     3.  Amendment to Section 2 of the Credit Agreement.
         ----------------------------------------------

         (a)  Subsection 2.9(a) of the Credit Agreement is hereby amended by
inserting the following after the end of clause (iii):

         "or (iv) the Sponsor in connection with (A) the transaction
     contemplated by Section 8(d) of the Third Amendment and (B) a transaction
     contemplated by the last sentence of the definition of "Consolidated
     EBITDA""

         (b)  Subsection 2.21 of the Credit Agreement is hereby deleted.
<PAGE>

                                                                               3


     4.  Amendment to Section 6 of the Credit Agreement.
         ----------------------------------------------

         (a)  Subsection 6.1 of the Credit Agreement is hereby amended by (i)
deleting the word, "and" at the end of clause (a), (ii) deleting the "." at the
end of clause (b) and (ii) inserting thereafter new clause (c) and (d) as
follows:

         "(c) as soon as available, but in any event not later than 30 days
     after the end of each month occurring during each fiscal year of the
     Borrower (other than the third, sixth, ninth and twelfth such month), the
     unaudited consolidated balance sheets of the Borrower and its consolidated
     Subsidiaries as of the end of such month and the related unaudited
     consolidated statements of income and of cash flows for such month and the
     portion of the fiscal year through the end of such month, setting forth in
     each case in comparative form the figures for the previous year, certified
     by a Responsible Officer as being fairly stated in all material respects
     (subject to normal year-end audit adjustments); and

         (d)  as soon as available, but in any event not later than February 15,
     2001, (i) unaudited versions of the financial statements listed in
     Subsection 6.1(a) and (ii) the corresponding certificate required by
     Subsection 6.2(b)."

         (b)  Section 6 of the Credit Agreement is hereby amended by inserting
the following subsection at the end of such section:

         "6.10  Financial Advisor. On and after November 15, 2000, the Borrower
                -----------------
     shall retain a financial advisor who is reasonably satisfactory to the
     Administrative Agent and who agrees to consult with the Administrative
     Agent and the Lenders from time to time."

     5.  Amendment to Section 7 of the Credit Agreement.
         ----------------------------------------------

         (a)  Subsection 7.1 of the Credit Agreement is hereby amended by adding
the following clause at the end of such Subsection:

         "(e)  Permit Consolidated EBITDA as at the end of any period set forth
     below to be less than the amount set forth below opposite such period:

Fiscal Period           Minimum EBITDA
-------------           --------------

7/1/00-9/30/00          $ 2,000,000

10/1/00-12/31/00        $ 8,300,000"

         (b)  Subsection 7.7 of the Credit Agreement is hereby amended by (i)
deleting therefrom the words "fiscal year" and inserting in lieu thereof the
words "fiscal period" and (ii) deleting the first two lines of the table in such
Subsection and inserting in lieu thereof the following lines :
<PAGE>

                                                                               4


     "7/1/00 - 9/30/00        $ 7,500,000
     10/1/00-12/31/00         $ 5,500,000"

     6.  Amendment to Section 8 of the Credit Agreement.
         ----------------------------------------------

         Section 8 of the Credit Agreement is hereby amended by:

         (a)  inserting after clause (k) the following new clauses (l) and (m):

         "(l) (i) any representation or warranty made by the Sponsor in any
     Loan Document or that is contained in any certificate, document or
     financial or other written statement furnished by it at any time under or
     in connection with any such Loan Document shall prove to have been
     inaccurate in any material respect on or as of the date made or deemed made
     or (ii) the Sponsor shall default in the observance or performance of any
     agreement contained in Section 8 of the Guarantee; or

         (m) Either or both of the Guarantee and the Sponsor Letter of Credit
     shall cease, for any reason other than as permitted by their respective
     terms, to be in full force and effect, or any Loan Party or any Affiliate
     of any Loan Party shall so assert, or;" and

         (b)  inserting in the last paragraph thereof the following clause (iii)
after clause (B)(ii):

         ", and (C) either or both of the following actions may be taken:  (i)
     with the consent of the Required Lenders, the Administrative Agent may, or
     upon the request of the Required Lenders, the Administrative Agent shall,
     declare the Guaranteed Amounts (as defined in the Sponsor Guarantee) due
     for all purposes of the Sponsor Guarantee; and (ii) upon the failure of the
     Sponsor to pay the Guaranteed Amounts within 15 days of a request
     therefore, the Administrative Agent shall draw under the Sponsor Letter of
     Credit (the proceeds of such drawing shall be applied to the reduction of
     the principal amount of the Loans in accordance with Section 2.9(d) and a
     corresponding reduction of the principal amount of the Guaranteed Loans (as
     defined in the Sponsor Guarantee))."

     7.  Sponsor Letter of Credit
         ------------------------

         The parties hereto hereby agree that upon any reduction in the
principal amount of the Guaranteed Loans (as defined in, and as determined in
accordance with Section 1(d) of, the Sponsor Guarantee), the Administrative
Agent shall deliver to The Chase Manhattan Bank, in its capacity as issuer of
the Sponsor Letter of Credit, a certificate, in the form set forth in the
Sponsor Letter of Credit, requesting that the principal amount of the Sponsor
Letter of Credit be reduced by an amount equal to such reduction.

     8.  Conditions to Effectiveness of this Amendment.
         ---------------------------------------------

         This Third Amendment shall become effective on and as of the date
hereof upon the satisfaction of the following conditions precedent (such date
the "Third Amendment Effective Date"):
     ------------------------------

         (a)  (i) The execution and delivery of the Third Amendment by the
Borrower, the Administrative Agent and the Required Lenders, (ii) the execution
and delivery of the Sponsor Guarantee by the Sponsor and (iii) the delivery of
the Sponsor Letter of Credit.
<PAGE>

                                                                               5


         (b)  The delivery of a legal opinion of Reboul, MacMurray, Hewitt,
Maynard & Kristol, counsel to the Sponsor, in form and substance satisfactory to
the Administrative Agent.

         (c)  The delivery of a copy of the financial statements of the Sponsor
for the most recently ended fiscal quarter evidencing the Sponsor's compliance
with Section 8(a) of the Sponsor Guarantee, together with a certificate of the
chief financial officer, treasurer or controller of the Sponsor, stating that
the Sponsor is in compliance with Section 8(a) of the Sponsor Guarantee.

         (d)  The receipt by the Borrower of not less than $15,000,000 in
proceeds from the issuance by the Borrower of its preferred stock to the Sponsor
on terms and conditions satisfactory to the Administrative Agent.

         (e)  The Borrower shall have paid all fees pursuant to Section 11 of
this Third Amendment.

         (f) The Administrative Agent shall have received a certificate of the
Borrower, dated the Third Amendment Effective Date, stating that the
representations and warranties contained in Section 8 of this Amendment are true
and correct on and as of such date.

     9.  Representations and Warranties
         ------------------------------

         (a)  No Default or Event of Default has occurred and is continuing
after giving effect to the amendments contemplated herein.

         (b)  Each of the representations and warranties made by the Loan
Parties and their Subsidiaries in or pursuant to the Loan Documents are true and
correct in all material respects on and as of the date hereof as if made on and
as of the date hereof, except for any representation and warranty which is
expressly made as of an earlier date, which representation and warranty shall
have been true and correct in all material respects as of such earlier date.

         (c)  The sum of the Tranche A Term Loans and Revolving Extensions of
Credit as of the date hereof is $88,569,420.00, and the Borrower is not aware of
any defenses, offsets or counterclaims it has with respect to such amounts
against the Lenders.
<PAGE>

                                                                               6


     10. Waiver. The Lenders hereby waive (a) any violation of any covenant set
         ------
forth in Section 7.1(a), (b) or (c) for the quarters ended June 30, 2000,
September 30, 2000 and December 31, 2000 and (b) any Event of Default which has
occurred or would occur by virtue of such violation. Any violation of any
covenant set forth in Section 7.1(a), (b) or (c) for the quarters ended June 30,
2000, September 30, 2000 and December 31, 2000 shall not be deemed an Event of
Default.

     11. Fees. The Borrower agrees to pay to each Lender which executes and
         ----
delivers this Third Amendment to the Administrative Agent on or prior to
September 22, 2000 an amendment fee in an amount equal to 0.375% of the amount
of each such Lender's pro rata share of the Commitments on and as of the Third
Amendment Effective Date, payable in immediately available funds on or before
the Third Amendment Effective Date.

     12. Miscellaneous.
         -------------

         (a)  Effect.  Except as expressly amended hereby, all of the
              ------
representations, warranties, terms, covenants and conditions of the Loan
Documents shall remain unamended and not waived and shall continue to be in
full force in effect.

         (b)  Counterparts.  This Third Amendment may be executed by one or
              ------------
more of the parties to this Third Amendment on any number of separate
counterparts, and all of said counterparts taken together shall be deemed to
constitute one and the same instrument. A set of the copies of this Third
Amendment signed by all the parties shall be lodged with the Borrower and the
Administrative Agent.

         (c)  Severability.  Any provision of this Third Amendment which is
              ------------
prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction,
be ineffective to the extent of such prohibition or unenforceability without
invalidating the remaining provisions hereof, and any such prohibition or
unenforceability in any jurisdiction shall not invalidate or render
unenforceable such provision in any other jurisdiction.

         (d)  Integration.  This Third Amendment and the other Loan Documents
              -----------
represent the agreement of the Loan Parties, the Administrative Agent and the
Lenders with respect to the subject matter hereof, and there are no promises,
undertakings, representations or warranties by the Administrative Agent or any
Lender relative to the subject matter hereof not expressly set forth or referred
to herein or in the other Loan Documents.

         (e)  GOVERNING LAW.  THIS THIRD AMENDMENT AND THE RIGHTS AND
              -------------
OBLIGATIONS OF THE PARTIES UNDER THIS THIRD AMENDMENT SHALL BE GOVERNED BY, AND
CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAW OF THE STATE OF NEW YORK.
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have caused this Third Amendment and
Waiver to be duly executed and delivered by their proper and duly authorized
officers as of the day and year first above written.

                                  BANCTEC, INC.

                                  By: /s/ Evelyn Henry Miller
                                      ------------------------------------------
                                      Name:  Evelyn Henry Miller
                                      Title:  Sr. V.P. & Chief Financial Officer

                                  THE CHASE MANHATTAN BANK, as Administrative
                                  Agent, Syndication Agent and as a Lender

                                  By: /s/ Craig Moore
                                      ------------------------------------------
                                      Name:
                                      Title:

                                  ABN AMRO BANK N.V., as Co-Agent and as a
                                  Lender

                                  By: /s/ Steven C. Wimpenny
                                      ------------------------------------------
                                      Name:  Steven C. Wimpenny
                                      Title:  Group Senior Vice President

                                  By: /s/ Parker H. Douglas
                                      ------------------------------------------
                                      Name:  Parker H. Douglas
                                      Title:  Group Vice President

                                  THE BANK OF NOVA SCOTIA

                                  By: /s/ F.C.H. Ashby
                                      ------------------------------------------
                                      Name:  F.C.H. Ashby
                                      Title:  Senior Manager Loan Operations

                                  BANK ONE, TEXAS, N.A.

                                  By: /s/ Randall B. Durant
                                      ------------------------------------------
                                      Name:  Randall B. Durant
                                      Title:  First Vice President
<PAGE>

                                  COMERICA BANK

                                  By: /s/ Mark B. Grover
                                      ------------------------------------------
                                      Name:  Mark B. Grover
                                      Title:  First Vice President

                                  GUARANTY FEDERAL BANK, F.S.B.

                                  By: /s/ Robert S. Hays
                                      ------------------------------------------
                                      Name:  Robert S. Hays
                                      Title:  Senior Vice President

                                  IBM CREDIT CORPORATION

                                  By: /s/ Thomas S. Curcio
                                      ------------------------------------------
                                      Name:  Thomas S. Curcio
                                      Title:  Manager of Commercial & Specialty
                                      Financing

                                  NATIONAL CITY BANK OF KENTUCKY

                                  By: /s/ Glenn E. Nord
                                      ------------------------------------------
                                      Name:  Glenn E. Nord
                                      Title:  Vice President

                                  WELLS FARGO BANK (TEXAS), N.A.

                                  By:
                                      ------------------------------------------
                                      Name:
                                      Title:
<PAGE>

                                                                       EXHIBIT A

                           FORM OF SPONSOR GUARANTEE
                           -------------------------
<PAGE>

                                                                       EXHIBIT B

                       FORM OF SPONSOR LETTER OF CREDIT
                       --------------------------------