COVER PAGE                                       
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549
                                       
                                 Schedule 13G
                                       
                   Under the Securities Exchange Act of 1934
                            (Amendment No. ____ )*

                       NATIONAL BANCORP OF ALASKA, INC.
- -------------------------------------------------------------------------------
(Name of Issuer)

                         COMMON STOCK, $2.50 PAR VALUE
- -------------------------------------------------------------------------------
                        (Title of Class of Securities)

                                  632587 10 1
- -------------------------------------------------------------------------------
                                (CUSIP Number)



Check the following box if a fee is being paid with this statement   [   ].  (A
fee is not required only if the filing person:  (1) has a previous statement on
file reporting beneficial ownership of more than five perpcent of the class of
securities described in Item 1; and (2) has filed no amendment subsequent
thereto reporting beneficial ownership of five percent or less of such class.)
(See Rule 13d-7.)

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities,
and for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
the Act but shall be subject to all other provisions of the Act (however, see
the Notes).

                       (Continued on following pages(s))

                               Page 1 of 5 Pages
 2

CUSIP No.  632587 10 1          13G                Page 2  of 5 Pages

1    NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON1

      Elmer E. Rasmuson


2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                      (a)   [  ]
                                                      (b)   [  ]
         n/a

3    SEC USE ONLY


4    CITIZENSHIP OR PLACE OF ORGANIZATION

         United States of America


                 5    SOLE VOTING POWER

  NUMBER OF               15,606,212
    SHARE
BENEFICIALLY     6    SHARED VOTING POWER
  OWNED BY
    EACH                  -0-
 REPORTING
   PERSON        7    SOLE DISPOSITIVE POWER
    WITH
                          15,606,212

                 8    SHARED DISPOSITIVE POWER

                          -0-

9    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

             15,606,212

10   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

             N/A

11   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

             50.8%

12   TYPE OF REPORTING PERSON*

             IN
**See footnote under Item 4, Ownership, on page 3 of this report.

                                       
                     *SEE INSTRUCTION BEFORE FILLING OUT!

 3

Item 1(a)   Name of Issuer:  National Bancorp of Alaska, Inc.

Item 1(b)   Address of Issuer's Principal Executive Office:
            301 West Northern Lights Boulevard
            Anchorage, AK  99503

Item 2(a)   Name of Person Filing:  Elmer E. Rasmuson

Item 2(b)   Business Address:
            PO Box 100600
            Anchorage, AK  99510-0600

Item 2(c)   Citizenship:  United States of America

Item 2(d)   Title of Class Securities:  Common Stock

Item 2(e)   CUSIP Number:  632587 10 1

Item 3      N/A

Item 4      Ownership:  *

Item 4(a)   Amount of Beneficially Owned:  15,606,212 shares

Item 4(b)   Percent of Class:  50.8%

Item 4(c)   Number of Shares to which such person has:

   (I)      Sole power to vote or to direct the vote 15,606,212 shares.

   (ii)     Shares power to dispose or to direct the vote -0-.

   (iii)    Sole power to dispose or to direct the disposition of 15,606,212.

   (iv)     Shares power to dispose or to direct the disposition of -0-.

* Included among the shares of Bank Common Capital Stock reported as
beneficially owned by Mr. Rasmuson are the following:

   (a)      Mr. Rasmuson has sole voting and dispositive powers over 3,116,640
            shares (10.1% of the outstanding shares) which he holds as trustee
            under three trusts for the benefit of each of his three adult
            children;





                                  Page 3 of 5

 4




Excluded among the shares of Bank Common Capital Stock reported as beneficially
owned by Mr. Rasmuson is the following:

   (b)      Mr. Rasmuson's wife has sole voting and dispositive power over
            135,752 shares (.4% of the outstanding shares) which she owns of
            record.

The filing of this Schedule 13G shall not be construed as an admission by Mr.
Rasmuson that he is, for purposes of Section 31(d) or 13(g) of the Securities
Exchange Act of 1934, the beneficial owner of the foregoing shares.

Mr. Rasmuson expressly disclaims beneficial ownership of the shares referenced
in (a) and (b) above.

Item 5      N/A

Item 6      Ownership of More Than 5 Percent on Behalf of Another Person:

            In reference to the trusts mentioned in Item 4 above, Mr. Rasmuson
            holds as trustee 1,038,880 shares of Common Stock (3.4%) for the
            benefit of each of his three adult children.  The beneficiaries
            have the right to receive or power to direct the receipt of
            dividends from the shares held by their respective trusts.

            None of the adult children have or share voting power or investment
            power over the shares by the trusts for their respective benefit.













                                  Page 4 of 5
5



Item 7      N/A

Item 8      N/A

Item 9      N/A

Item 10     N/A

After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.





         1-4-99                               /s/Elemer E. Rasmuson
- -----------------------                       ------------------------
         (Date)                               (Signature)

                                              Elmer E. Rasmuson
                                              (Name)





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