SECURITIES AND EXCHANGE COMMISSION
                          WASHINGTON, D.C.  20549


                                  FORM 10-K

(Mark One)

/ x / ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF 
      THE SECURITIES EXCHANGE ACT OF 1934
      For the fiscal year ended December 31, 1998 or

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

      Commission File No.:   333-65481-03   

               Norwest Asset Securities Corporation
                Mortgage Pass-Through Certificates
                  Series  1998-34       Trust       
        (Exact name of registrant as specified in its charter)



New York                             Pending
(State or other jurisdiction     (I.R.S. Employer 
 of incorporation or              Identification  No.)
 organization)

c/o Norwest Bank Minnesota, N.A.
11000 Broken Land Parkway
Columbia, Maryland                            21044
(Address of principal executive offices)     (ZIP Code)


Registrant's telephone number, including area code: 
     (410) 884-2000

Securities to be registered pursuant to Section 12(b)
of the Act:  

     NONE

Securities to be registered pursuant to Section 12(g) 
of the Act:  

     NONE

Indicate by check mark whether the registrant (1) has filed all
reports required to be filed by Section 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 ___


Indicate by check mark if disclosure of delinquent filers pursuant
to item 405 of Regulation S-K is not contained herein, and will
not be contained, to the best of registrant's knowledge, in 
definitive proxy or information statements incorporated by
reference in Part III of this Form 10-K or any amendment to this
Form 10-K.

     Not applicable


State the aggregate market value of the voting and non-voting
common equity held by non-affiliates of the registrant.  
The aggregate market value shall be computed by reference to 
the price at which the common equity was sold, or the average
bid and asked prices of such common equity, as of a specified
date within 60 days prior to the date of filing.  (See
definition of affiliate in Rule 12b-2 of the Exchange Act.)

     Not applicable


Indicate the number of shares outstanding of each of the
registrant's classes of common stock, as of the latest 
practicable date.

     Not applicable


                                        Part I

Item 1.  Business.

         Omitted

Item 2.  Properties.

         See Item 14(a), Exhibits 99.1, 99.2, and 99.3, for 
         information provided in lieu of information required by 
         Item 102 of Regulation S-K.

Item 3.  Legal Proceedings.

         The registrant knows of no material pending legal 
         proceedings involving the trusts created under the
         Pooling and Servicing Agreement (the Trusts), the
         Trustee, the Servicer or the registrant with respect to
         the Trusts other than routine litigation incidental to
         the duties of the respective parties.

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

         None


                             PART II

Item 5.  Market for Registrant's Common Equity and Related
         Stockholder Matters.  

         No established public trading market for the
         Certificates exists.

         As of December 31, 1998, the number of holders of
         the publicly offered Certificates was
         24


Item 6.  Selected Financial Data.

         Omitted

Item 7.  Management's Discussion and Analysis of Financial
         Condition and Results of Operations.

         Omitted

Item 8.  Financial Statements and Supplementary Data.

         See Item 14(a), Exhibits 99.1, 99.2, 99.3, for
         information provided in lieu of information required 
         by Item 302 of Regulation S-K.

Item 9.  Changes in and Disagreements with Accountants on
         Accounting and Financial Disclosure.

         None.



                           PART III

Item 10.  Directors and Executive Officers of the Registrant.

          Not applicable.

Item 11.  Executive Compensation.

          Not applicable.

Item 12.  Security Ownership of Certain Beneficial Owners and
          Management.

          Not applicable.

Item 13.  Certain Relationships and Related Transactions.

          Not applicable.


                             PART IV

Item 14.  Exhibits, Financial Statement Schedules, and Reports
          on Form 8-K.

          (a) Exhibits
          
              (99.1) Annual Independent Accountants' Servicing
                     Reports concerning servicing activities for 
                     the year ended December 31, 1998.

                     a)   AMERICA FIRST CREDIT UNION <F1>
                     b)   BANCOKLAHOMA MTG <F1>
                     c)   BANK OF AMERICA <F1>
                     d)   BANK UNITED <F1>
                     e)   COLUMBIA NATIONAL INC <F1>
                     f)   COUNTRYWIDE FUNDING <F1>
                     g)   FIRST UNION MTG CORP <F1>
                     h)   GMAC MTG CORP <F1>
                     i)   HIBERNIA NATIONAL BANK <F1>
                     j)   HOME SAVINGS OF AMERICA <F1>
                     k)   HOMESIDE LENDING INC (FL) <F1>
                     l)   HUNTINGTON MTG CO <F1>
                     m)   MARINE MIDLAND BANK <F1>
                     n)   MERRILL LYNCH CREDIT CORP <F1>
                     o)   NATIONAL CITY MTG CO <F1>
                     p)   NORWEST MTG INC <F1>
                     q)   SUN TRUST MTG INC <F1>   

              (99.2) Report of Management as to Compliance with
                     Minimum Servicing Standards for the year
                     ended December 31, 1998.

                     a)   AMERICA FIRST CREDIT UNION <F1>
                     b)   BANCOKLAHOMA MTG <F1>
                     c)   BANK OF AMERICA <F1>
                     d)   BANK UNITED <F1>
                     e)   COLUMBIA NATIONAL INC <F1>
                     f)   COUNTRYWIDE FUNDING <F1>
                     g)   FIRST UNION MTG CORP <F1>
                     h)   GMAC MTG CORP <F1>
                     i)   HIBERNIA NATIONAL BANK <F1>
                     j)   HOME SAVINGS OF AMERICA <F1>
                     k)   HOMESIDE LENDING INC (FL) <F1>
                     l)   HUNTINGTON MTG CO <F1>
                     m)   MARINE MIDLAND BANK <F1>
                     n)   MERRILL LYNCH CREDIT CORP <F1>
                     o)   NATIONAL CITY MTG CO <F1>
                     p)   NORWEST MTG INC <F1>
                     q)   SUN TRUST MTG INC <F1>   

              (99.3) Annual Statements of Compliance under the
                     Pooling and Servicing Agreements for the
                     year ended December 31, 1998.

                     a)   AMERICA FIRST CREDIT UNION <F1>
                     b)   BANCOKLAHOMA MTG <F1>
                     c)   BANK OF AMERICA <F1>
                     d)   BANK UNITED <F1>
                     e)   COLUMBIA NATIONAL INC <F1>
                     f)   COUNTRYWIDE FUNDING <F1>
                     g)   FIRST UNION MTG CORP <F1>
                     h)   GMAC MTG CORP <F1>
                     i)   HIBERNIA NATIONAL BANK <F1>
                     j)   HOME SAVINGS OF AMERICA <F1>
                     k)   HOMESIDE LENDING INC (FL) <F1>
                     l)   HUNTINGTON MTG CO <F1>
                     m)   MARINE MIDLAND BANK <F1>
                     n)   MERRILL LYNCH CREDIT CORP <F1>
                     o)   NATIONAL CITY MTG CO <F1>
                     p)   NORWEST MTG INC <F1>
                     q)   SUN TRUST MTG INC <F1>   

              (99.4) Aggregate Statement of Principal and
                     Interest Distributions to Certificate
                     Holders.

                     No distributions were made to Certificate 
                     Holders during the fiscal period covered by
                     this report.

            (b)  No reports on Form 8-K have been filed during
                 the last quarter of the period covered by 
                 this report.

            (c)  Not applicable.

            (d)  Omitted.

<F1>  Such document (i) is not filed herewith since such document 
was not received by the reporting person at least three business 
days prior to the due date covered by this report:  and (ii) will 
be included in an amendment to this report on Form 10-K/A to be 
filed within 30 days of the Reporting Person's receipt of such 
document.

                           SIGNATURES

Pursuant to the requirements of Section 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:

Norwest Asset Securities Corporation
Mortgage Pass-Through Certificates
Series  1998-34 Trust       

Signed:   Norwest Bank Minnesota, N.A., as Master Servicer  

By:   Sherri J. Sharps, Vice President                  
By:  /s/  Sherri J. Sharps, Vice President                  

Dated:  March 20, 1999



SUPPLEMENTAL INFORMATION TO BE FURNISHED WITH REPORTS FILED
PURSUANT TO SECTION 15(d) OF THE ACT BY REGISTRANTS WHICH HAVE NOT
REGISTERED SECURITIES PURSUANT TO SECTION 12 OF THE ACT.

(a)(i)   No annual report is provided to the Certificateholders 
other than with respect to aggregate principal and interest
distributions.

(a)(ii)  No proxy statement, form of proxy or other proxy
soliciting material has been sent to any Certificateholder
with respect to any annual or other meeting of Certificateholders.