**SECURITIES AND EXCHANGE COMMISSION****Washington, D.C.  20549****UNITED STATES****FORM 10-K****[ X ] ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934****[    ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934**(Exact Name of Registrant as Specified in its Charter)(State or Other JurisdictionOf Incorporation)Registrant's telephone number, including area code:**Credit Suisse First Boston Mortgage Securities Corp. Home Equity Asset Trust 2005-4****Credit Suisse First Boston Mortgage Securities Corp.****Delaware**(I.R.S. EmployerIdentification No.)**13-3320910**Commission File Number :**333-120966-20**(Address of Principal Executive Offices)**New York, New York****11 Madison Avenue**(Zip Code)**10010**(212) 325-2000Securities registered pursuant to Section 12(b) of the Act:NoneIndicate by check mark if the registrant is a well-known seasoned issuer, as defined in Rule 405 of the Securities Act.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. For the fiscal year ended December 31, 2005orFor the transition period from _____________ to _____________(Issuing Entity)Securities registered pursuant to Section 12(g) of the Act:NoneIndicate by check mark  if the registrant is not required to file reports pursuant to Section 13 or Section 15(d) of the Act.Indicate by check mark  if disclosure of delinquent filers pursuant to Item 405 of Regulation S-K ( 229.405 of this chapter) 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.                      Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, or a non-accelerated filer.Indicate by check mark whether the registrant is a shell company (as defined in Rule 12b-2 of the Act).**[  Yes]****Home Equity Pass-Through Certificates****Series 2005-4**Documents incorporated by reference:**None**State the aggregate market value of the voting and non-voting common equity held by non-affiliates computed by reference to the price at which the common equity was last sold, or the average bid and asked price of such common equity, as of the last business day of the registrant's most recently completed second fiscal quarter. **Not Applicable.****[X No]****[  Yes] [X No]****[X Yes] [  No]****[X]****[  Yes] [X No]****Large accelerated filer [ ]****Accelerated filer [ ]****Non-accelerated filer [X]**(Exact Name of Depositor as Specified in its Charter)(Exact Name of Sponsor as Specified in its Charter)**Credit Suisse First Boston Mortgage Securities Corp.****PART I****Item 1. Business.**Not Applicable.**Item 1A. Risk Factors.****Item 1B. Unresolved Staff Comments.****Item 2. Properties.****Item 3. Legal Proceedings.**There were no legal proceedings.**Item 4. Submission of Matters to a Vote of Security Holders.**There were no matters submitted to a vote of the Security Holders.Not Applicable.Not Applicable.Not Applicable.**Item 5. Market for Registrant's Common Equity, Related Stockholder Matters and Issuer Purchases of Equity Securities.****Item 6. Selected Financial Data.**No established public trading market for the Certificates exists.**Item 7. Management's Discussion and Analysis of Financial Condition and Results of Operation.****Item 7A. Quantitative and Qualitative Disclosures About Market  Risk.****Item 8. Financial Statements and Supplementary Data.****Item 9. Changes in and Disagreements With Accountants on Accounting and Financial Disclosure.****Item 9A. Controls and Procedures.****Item 9B. Other Information.**Not Applicable.**PART II**Not Applicable.Not Applicable.Not Applicable.Not Applicable.Not Applicable.Not Applicable.There are approximatelyholders of record as of the end of the reporting year. Fifty-seven (57)**Item 10. Directors and Executive Officers of the Registrant.****Item 11. Executive Compensation.****Item 12. Security Ownership of Certain Beneficial Owners and Management and Related Stockholder Matters.****Item 13. Certain Relationships and Related Transactions.****Item 14. Principal Accounting Fees and Services.****PART III**Not Applicable.Not Applicable.Not Applicable.Not Applicable.Not Applicable.**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.By (Signature and Title):Date(Registrant):**Credit Suisse First Boston Mortgage Securities Corp.****03-29-06****/s/ Bruce Kaiserman****Bruce Kaiserman****Vice President**a)    1. Not Applicable.**Item 15. Exhibits, Financial Statement Schedules.**       2. Not Applicable.       3. Exhibits.b)    See (a) 3 above.c)    Not Applicable.**PART IV**       31.1 Sarbanes-Oxley Certification       99.1 Independent Accountant's Servicing Report for the year ended December 31, 2005       99.2 Report of Management as to compliance with minimum servicing standards for the year ended December 31, 2005       99.3 Annual Statement of Compliance for the year ended December 31, 2005a) Select Portfolio Servicing, Inc., as Servicerb) Wells Fargo Home Mortgage, Inc., as Servicera) Select Portfolio Servicing, Inc., as Servicerb) Wells Fargo Home Mortgage, Inc., as Servicera) Select Portfolio Servicing, Inc., as Servicerb) Wells Fargo Home Mortgage, Inc., as Servicer**Exhibit    Index**       31.1 Sarbanes-Oxley Certification       99.1 Independent Accountant's Servicing Report for the year ended December 31, 2005       99.2 Report of Management as to compliance with minimum servicing standards for the year ended December 31, 2005       99.3 Annual Statement of Compliance for the year ended December 31, 2005a) Select Portfolio Servicing, Inc., as Servicerb) Wells Fargo Home Mortgage, Inc., as Servicera) Select Portfolio Servicing, Inc., as Servicerb) Wells Fargo Home Mortgage, Inc., as Servicera) Select Portfolio Servicing, Inc., as Servicerb) Wells Fargo Home Mortgage, Inc., as Servicer