<PAGE>   1
                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                             Washington, DC  20549


                                   FORM 10-Q

(Mark One)

[X]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
     SECURITIES EXCHANGE ACT OF 1934.

For the quarterly period ended     March 31, 2000

                                      OR

[ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
     EXCHANGE ACT OF 1934

For the transition period from                     to


Commission File Number 0-10769


                   National Bancorp of Alaska, Inc.
-----------------------------------------------------------------------
      (Exact name of registrant as specified in its charter)

          Delaware                           92-0087646
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 (State of other jurisdiction of           (IRS Employer
  incorporation or organization)         Identification No.)

   Northern Lights Boulevard and C Street, Anchorage, AK  99503
-----------------------------------------------------------------------
  (Address of principal executive offices)               (Zip Code)

                         (907) 276-1132
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    (Registrant's telephone number, including area code)

Indicate by check mark whether the registrant (1) has filed all  reports
required to be filed by Sections 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or  for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing  requirements for the past 90 days.    YES  X        NO___

The registrant has one class of Common Stock, $2.50 par value.
Number of shares outstanding as of May 10, 2000:    30,224,177



PAGE>   2
                               Table of Contents

                                                                      Page

                                    Part I

Item 1   Financial Statements............................................3

Item 2   Management's Discussion and Analysis of Financial
         Condition and Results of Operations.............................8

                                    Part II

Item 1   Legal Proceedings..............................................13

Item 2   Changes in Securities..........................................13

Item 3   Defaults Upon Senior Securities................................13

Item 4   Submission of Matters to a Vote of Security Holders............13

Item 5   Other Information..............................................13

Item 6   Exhibits and Reports on Form 8-K...............................13


























                                      -2-
<PAGE>   3
ITEM 1.  FINANCIAL STATEMENTS.

                 CONSOLIDATED STATEMENTS OF INCOME (Unaudited)

(In Thousands Except Statistics) Three Months Ended March 31
                                                  2000         1999
INTEREST INCOME:
  Loans & Lease Financing Including Fee         $40,845     $36,747
  Balances with Banks                                 3           -
  Federal Funds Sold                                251         464
  Investment Securities Including Dividends
    U.S. Government                               2,087       2,226
    U. S. Agencies                                6,846       6,591
    States & Political Subdivisions                 204         198
    Mortgage and Asset-Backed Securities          4,034       4,199
    Other Securities                              1,821       1,751
-------------------------------------------------------------------
      TOTAL INTEREST INCOME                      56,091      52,176

INTEREST EXPENSE:
  Deposits                                       14,346      13,713
  Federal Funds Purchased & Securities Sold
    Under Agreement to Repurchase                 5,239       3,789
  Other Purchased Funds                               2           2
-------------------------------------------------------------------
      TOTAL INTEREST EXPENSE                     19,587      17,504
-------------------------------------------------------------------
      NET INTEREST INCOME                        36,504      34,672
  Provision for Loan Losses                       1,200       1,200
-------------------------------------------------------------------
      NET INTEREST INCOME AFTER
      PROVISION FOR LOAN LOSSES                  35,304      33,472

OTHER INCOME:
  Trust Department Income                           711         712
  Service Charges on Deposit Accounts             3,613       3,363
  Loan Servicing Fees                             2,671       2,491
  Securities Transactions                        (1,515)          -
  Net gains on Limited Partnership Investments    4,151         331
  Credit Card Service Fees                        1,910       1,610
  Other                                           4,380       4,546
-------------------------------------------------------------------
     TOTAL OTHER INCOME                          15,921      13,053

OTHER EXPENSE:
  Salaries                                       11,461      10,628
  Profit Sharing & Other Employee Benefits        3,666       3,510
  Net Occupancy Expense of Bank Premises          1,971       1,995
  Furniture & Equipment Expense                   1,859       2,156
  Other                                           9,682       8,453
-------------------------------------------------------------------
      TOTAL OTHER EXPENSE                        28,639      26,742

Income Before Income Taxes                       22,586      19,783
Applicable Income Taxes                           8,134       7,063
-------------------------------------------------------------------
      NET INCOME                                $14,452     $12,720
===================================================================
Per Share Statistics
  Net Income                                    $  0.48     $  0.42
===================================================================
  Average Number of Shares Outstanding       30,224,177  30,560,760
  (See note to consolidated statements.)



                                      -3-
<PAGE>   4
                CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(In Thousands Except Statistics) Three Months Ended March 31
                                                           2000      1999
Net income                                               $14,452   $12,720
Other comprehensive income, net of taxes:
  Unrealized losses securities:
    Unrealized holding losses arising during period       (1,484)     (642)
    Less: reclassification adjustment for
          losses included in net income                     (892)        -
--------------------------------------------------------------------------
   Other comprehensive income                               (592)     (642)
--------------------------------------------------------------------------
Comprehensive Income                                     $13,860   $12,078
==========================================================================




































                                      -4-
<PAGE>   5
<TABLE>
<CAPTION>
                CONSOLIDATED STATEMENTS OF CONDITION  (Unaudited)

                                                                    March 31      December 31
(In Thousands Except Statistics)                                 2000       1999       1999
<S>                                                         <C>        <C>        <C>
ASSETS:
  Cash and Due from Banks                                   $  142,182 $  139,755 $  151,703
  Interest-Bearing Balances with Banks                             309        155        253
  Securities Purchased under agreement to resell                     -    126,000     25,000
  Investment Securities:
    U. S. Agencies                                             356,811    326,421    376,652
    States and Political Subdivisions                           18,682     18,108     22,558
    Mortgage and Asset-Backed Securities                       234,536    237,104    248,188
    Other Securities                                            46,392     60,110     58,493
--------------------------------------------------------------------------------------------
      Total Investment Securities                              656,421    641,743    705,891
      (Market Value $642,372 in 2000)
  Securities Available for Sale at Market                      247,898    222,243    258,159

  Loans and Lease Financing                                  1,666,848  1,502,589  1,656,562
  Reserve for Loan Losses                                      (26,714)   (25,690)   (27,565)
--------------------------------------------------------------------------------------------
    Net Loans and Lease Financing                            1,640,134  1,476,899  1,628,997

  Loans Held for Sale                                           51,931     71,553     66,478

  Net Premises and Equipment                                    68,348     71,415     69,392
  Limited partnership investments                               86,528     76,533     69,658
  Other Assets                                                  80,580     64,374     77,974
--------------------------------------------------------------------------------------------
      Total Assets                                          $2,974,331 $2,890,670 $3,053,505
============================================================================================
LIABILITIES AND SHAREHOLDERS' EQUITY:
  Demand Deposits                                          $   587,438$   572,783$   605,620
  Interest-Bearing Deposits:
    NOW                                                        237,186    222,792    236,252
    Savings                                                    297,970    297,912    313,397
    Money Market Savings                                       304,582    305,823    321,749
    Time                                                       644,938    674,214    680,799
--------------------------------------------------------------------------------------------
      Total Interest-Bearing Deposits                        1,484,676  1,500,741  1,552,197
--------------------------------------------------------------------------------------------
      Total Deposits                                         2,072,114  2,073,524  2,157,817

  Federal Funds Purchased                                       14,048        242      1,332
  Securities Sold Under Agreement to Repurchase                384,222    350,637    404,456
  Other Purchased Funds                                             93        165        110
  Other Liabilities                                             43,156     45,270     38,418
--------------------------------------------------------------------------------------------
      Total Liabilities                                      2,513,633  2,469,838  2,602,133

  Shareholders' Equity                2000        1999
    Common Stock - $2.50 Par Value                              80,000     80,000     80,000
     Shares Authorized            40,000,000  40,000,000
     Shares Outstanding           32,000,000  32,000,000
    Capital Surplus                                             63,106     63,099     63,106
    Retained Earnings                                          361,415    315,707    351,497
    Net Unrealized Gains on
      Available-for-Sale Securities, Net of Tax                 (1,666)     1,992     (1,074)
    Treasury Stock at Cost
     (1,775,823 Shares on March 31, 2000 and
      1,691,817 Shares on March 31, 1999)                      (42,157)   (39,966)   (42,157)
--------------------------------------------------------------------------------------------
      Total  Shareholders' Equity                              460,698    420,832    451,372
--------------------------------------------------------------------------------------------
      Total Liabilities and Shareholders Equity             $2,974,331 $2,890,670 $3,053,505
============================================================================================
Per Share Statistics
Net Book Value                                                  $15.24     $13.89     $14.93
============================================================================================
</TABLE>
(See note to consolidated statements.)
                                       -5-
<PAGE>   6
               CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited)


(In Thousands) Three Months Ended March 31         2000     1999

OPERATING ACTIVITIES:
  Net Income                                               $ 14,452  $ 12,720
  Adjustments to Reconcile Net Income to Net Cash
  Provided by Operating Activities:
    Provision for Loan Losses                                 1,200     1,200
    Deferred Taxes Expense (Credit)                              34      (201)
    Depreciation and Amortization                             2,002     2,112
    Net amortization on Securities                              288        88
    Gain on Security and Limited Partnership Transactions    (4,353)     (331)
    Loss on Security and Limited Partnership Transactions     1,717         -
    Loss (Gain) on Loan Sales                                    10      (483)
    Loss (Gain) on Sales of Premises and Equipment               (2)        1
    Gain on Sale of Other Assets                                 42         -
    Net Decrease in Loans Held for Sale                      14,537    73,665
    Decrease in Interest Receivable, Prepaid Expense,
      and Other Assets                                          242       194
    Increase in Interest Payable, Accrued
      Expenses and Other Liabilities                          4,738     4,667
-----------------------------------------------------------------------------
        Net Cash Provided by Operating Activities            34,907    93,632

INVESTING ACTIVITIES:
  Net Decrease (Increase) in Federal Funds Sold, and
    Interest Bearing Deposits with Other Banks               24,944  (126,039)
  Proceeds from Maturities of Securities Held to Maturity    49,681   141,327
  Purchases of Securities Held to Maturity                     (432)   (8,080)
  Proceeds from Maturities of Securities Available for Sale      37    26,394
  Purchases of Securities Available for Sale                      -   (10,315)
  Proceeds from Securities Available for Sale                 7,636         -
  Net Increase in Loans and Lease Financing                 (12,781)  (15,750)
  Proceeds from Sales of Premises and Equipment                   3         2
  Purchases of Premises and Equipment                          (579)   (2,921)
  Proceeds from Sale of Limited Partnership Investments       2,314       367
  Purchases of Limited Partnership Investments              (16,587)   (5,153)
  Acquisition of NBA Insurance Services LLP                       -    (3,500)
  Proceeds from Sale of Other Assets                            802         -
  Purchases of Other Assets                                  (1,694)   (1,309)
-----------------------------------------------------------------------------
        Net Cash Provided by (Used in) Investing Activities  53,344    (4,977)

FINANCING ACTIVITIES:
  Net Decrease in Total Deposit                             (85,703)  (63,432)
  Net Decrease in Short-Term Borrowings                      (7,535)  (24,953)
  Acquisition of Treasury Stock                                   -    (9,167)
  Proceeds from Sale of Treasury Stock                            -       116
  Cash Dividends Paid                                        (4,534)   (4,607)
-----------------------------------------------------------------------------
        Net Cash Used in Financing Activities               (97,772) (102,043)
-----------------------------------------------------------------------------
        Decrease in Cash and Cash Equivalents                (9,521)  (13,388)

  Cash and Cash Equivalents at Beginning of Year            151,703   153,143
-----------------------------------------------------------------------------
        Cash and Cash Equivalents at End of  March         $142,182  $139,755
=============================================================================

                                      -6-
<PAGE>   7
                          National Bancorp of Alaska
                Notes to the Consolidated Financial Statements
                                  (Unaudited)

     Note A - Basis of Presentation

     The accompanying unaudited consolidated financial statements have been
     prepared in accordance with generally accepted accounting principles for
     interim financial information and with the instructions and regulations
     for filing Form 10-Q.  Operating results for the three-month period ended
     March 31, 2000, are not necessarily indicative of the results that may be
     expected for the year ending December 31, 2000.

     The statements should be read in conjunction with the summary of
     accounting policies and notes to the financial statements included in the
     Registrant's annual report for the year ended December 31, 1999.  In the
     opinion of management, all adjustments (consisting of normal recurring
     accruals necessary for a fair presentation) have been included.

































                                      -7-
<PAGE>   8
 Item 2. Management Discussion and Analysis of Financial Condition and Results
                                 of Operations

National Bancorp of Alaska (the Corporation) recorded earnings of $14.45
million in the first quarter of 2000 compared to $12.72 million for the first
quarter of 1999.  Earnings per share were $0.48 as of March 31, 2000 up 14%
from the $0.42 earned through March 31, 1999.

Return on average assets using annualized income from operations plus year-to-
date net security gains and nonrecurring loan loss recoveries was 1.79% for the
three-month period ended March 31, 2000, compared to 1.78% for the three-month
period ended March 31, 1999.  The annualized return on average stockholders'
equity was 11.69% for the first three months of 2000.

Net interest income increased $1,832,000 after the provision for loan losses
during the first three months of 2000 compared to the same period during the
previous year.  The increase is due to increase of interest income on earning
assets.  Interest on earning assets increased $3,915,000 from the first quarter
of 1999 to the first quarter of 2000, while interest expense increased
$2,083,000.

The provision for loan loss was $1,200,000 at March 31, 2000, compared to a
provision for loan losses $1,200,000 at March 31, 1999.  The reserve for loan
loss was 1.60% of outstanding loans at March 31, 2000 and 1.71% at March 31,
1999 and 1.66% at December 31, 1999.  Nonperforming assets, defined as other
real estate owned, nonaccrual loans, restructured loans, and loans past due 90
days and still accruing, as a percentage of total loans and other real estate
owned decreased to 0.65%  at March 31, 2000 from 0.70% at March 31, 1999, and
decreased from 0.77% at December 31, 1999.

Non-interest income increased $2,868,000 for the first quarter from the same
period in 1999 due to the increase in net gains on limited partnership
investment partially offset with net security losses.  Non-interest expense
increased by $1,897,000 over the first quarter of 1999 with $989,000 attributed
to personnel and benefits expenses.  Other non-interest expense increased
$1,229,000, which includes $461,000 in real estate, legal and accounting fees
related to the Wells Fargo merger.

Material Changes in Financial Condition

Total assets at March 31, 2000, were $2,974,331,000 an increase of 2.9% or $84
million from the same period one year earlier, and an decrease of $79 million
or 2.6% from December 31, 1999.  Investment securities and securities available
for sale have increased by $40 million over the first quarter of 1999.  Loans
and leases and loans held for sale have increased $145 million over the same
period in 1999.  Limited partnership investments increased $10 million over the
first quarter of 1999. Total deposits have decreased by $1 million from March
31, 1999, and decreased by $86 million from December 31, 1999.

Liquidity

The Corporation maintains sufficient excess liquidity to satisfy contractual
liabilities, meet withdrawal requirements of depositors, fund operations, and
provide for customers' credit needs.  Management knows of no demand,
commitments, or events that would result in liquidity changing in a material
amount.


                                      -8-
<PAGE>   9
Capital Resources

Shareholders' equity increased by $9.3 million from December 31, 1999, to
$460.7 million at March 31, 2000.  Federal regulatory agencies have established
capital adequacy guidelines setting a minimum for Tier 1, total capital and
leverage ratios which were 4%, 8% and 3%, respectively.  The Corporation's and
National Bank of Alaska"s ratios are as follows:

                                                    March 31     December 31
                                                2000      1999      1999
 Tier 1 Risk Based Capital Ratio
   National Bancorp of Alaska, Inc.             18.69%    18.29%    18.02%
   National Bank of Alaska                      11.18     11.86     11.66
 Total Risk Based Capital Ratio
   National Bancorp of Alaska, Inc.             19.78%    19.43%    19.14%
   National Bank of Alaska                      12.36     13.09     12.85
 Leverage Ratio
   National Bancorp of Alaska                   15.33%    14.51%    14.46%
   National Bank of Alaska                       8.89      9.04      9.01























                                      -9-
<PAGE>  10
Statistical Disclosures

Selected Guide 3-Statistical Disclosure by Bank Holding Companies

III. Loan Portfolio
  C.  Risk Elements

Nonperforming Assets
                                                   March 31      December 31
(In Thousands)                                  2000      1999      1999
Nonaccrual
  Commercial and industrial                 $ 6,925   $ 2,321   $ 8,996
  Real estate construction                        -         -       140
  Real estate long-term                       1,527     4,465       826
  Other                                          41         -         -
-----------------------------------------------------------------------
     Total                                    8,493     6,786     9,962
-----------------------------------------------------------------------
Restructured Loans
  Real estate long-term                           -         -         -
-----------------------------------------------------------------------
     Total                                        -         -         -
-----------------------------------------------------------------------
Accruing loans past due 90 days or more       1,468     3,039     1,884
-----------------------------------------------------------------------
Other real estate owned                         840       723       840
-----------------------------------------------------------------------
Total nonperforming assets                  $10,801   $10,548   $12,686

Nonperforming assets as a percentage
of loans and leases and other real
estate owned at end of period                  0.65%     0.70%     0.77%


Potential Problem Loans

At March 31, 2000, an additional $59,405,000 in loans are being closely
monitored by management.  These loans are not included in any category of non-
performing loans.  However, management has concerns about the borrower's
abilities to comply with their present loan repayment terms.  These loans are
reviewed monthly to assess any change in collectability.






                                     -10-
<PAGE>  11
IV.  Summary of Loan Loss Experience

   A:  Analysis of Reserve for Loan Loss
(In Thousands)                              March 31, 2000   December 31, 1999
Balance January 1                              $27,565           $24,678
Provision charged to operations                  1,200             4,950
Recoveries on loans previously charged off       1,043             4,165
Less loans charged off                          (3,094)           (6,228)
------------------------------------------------------------------------
Balance at end of period                       $26,714           $27,565
========================================================================
Composition of Loan Charge Off and Recoveries
Loans Charged Off:
Commercial loans and leases                    $ 1,848          $  1,880
Real estate construction                            20                 -
Real estate long-term                               46                41
Consumer                                           888             3,383
Visa                                               292               924
------------------------------------------------------------------------
     Total Charge Offs                           3,094             6,228

Recoveries:
Commercial loans and leases                         60               792
Real estate construction                             -               194
Real estate long-term                               58               794
Consumer                                           838             1,972
Visa                                                87               224
Nontaxable                                           -               189
------------------------------------------------------------------------
     Total Recoveries                            1,043             4,165
------------------------------------------------------------------------
     Net Charge Offs                           $ 2,051           $ 2,063
========================================================================
















                                     -11-

B.  Allocation of the Allowance for Loan Loss

                                                     Allocation of Reserves
                                                       To Loan Categories
                                                    --------------------------
                              Loan Category As a %  % of Total       Amount of
                                    of Total Loans     Reserve Reserves(000's)

March 31, 2000

Commercial and Industrial                    39.8%        5.6%        $ 1,495
Real Estate Construction                      4.3         0.1              33
Real Estate Long Term                        29.3         0.6             149
Installment                                  22.1        32.1           8,581
Nontaxable                                    4.1           -               -
Lease Financing                               0.4           -               -
Unallocated                                     -        61.6          16,456
-----------------------------------------------------------------------------
                                            100.0%      100.0%        $26,714


December 31, 1999

Commercial and Industrial                    39.1%        7.8%       $  2,148
Real Estate Construction                      5.3         0.2              57
Real Estate Long Term                        29.3         1.1             312
Installment                                  21.8        33.4           9,194
Nontaxable                                    4.0           -               -
Lease Financing                               0.5           -               -
Unallocated                                     -        57.5          15,854
-----------------------------------------------------------------------------
                                            100.0%      100.0%        $27,565


















                                     -12-

<PAGE>  13
                          PART II - OTHER INFORMATION

Item 1:    Legal Proceedings
           Not applicable.

Item 2:    Changes in Securities
           Not applicable.

Item 3:    Defaults Upon Senior Securities
           Not applicable.

Item 4:    Submission of Matters to a Vote of Security Holders
           Not applicable

Item 5:    Other Information
           Not applicable.

Item 6:    Exhibits and Reports on Form 8-K
           (a)  Exhibits
                Exhibit 27.  Financial Data Schedule

           (b)  Reports on Form 8-K
                There were three Form 8-K's during the quarter ended
                March 31, 2000.

                On January 12, 2000, a Form 8-K reported the signing of a
                definitive agreement and plan of reorganization for the merger
                of the Corporation and Wells Fargo and Company.

                On February 15, 2000, a Form 8-K reported an amendment to the
                Corporation's and Wells Fargo & Company's agreement and plan of
                reorganization dated as of January 12, 2000 to redefine "Wells
                Fargo Measurement Price".

                On March 30, 2000, a Form 8-K reported the "Wells Fargo
                Measurement Price" and rate of exchange of Wells Fargo &
                Company common stock for the Corporation's common stock.
















                                     -13-
<PAGE>  14

                                  SIGNATURES


Pursuant to the requirements of Sections 13 or 15(d) of the Securities Exchange
Act of 1934, the registrant has duly caused this report to be signed on its
behalf by the undersigned, thereunto duly authorized.



                                           NATIONAL BANCORP OF ALASKA, INC.



      May 12, 2000                         /s/Edward B. Rasmuson
          Date                             Edward B. Rasmuson, Chairman
                                           of the Board

      May 12, 2000                         /s/Richard Strutz
          Date                             Richard Strutz, President

      May 12, 2000                         /s/Gary Dalton
       Date                                Gary Dalton, Executive Vice
                                           President and Controller
                                           (Principal Accounting Officer)





















                                     -14-