Mayor Walter E. Washington will make public today, three long-awaited fact-finding reports on allegations of nepotism and cronyism in hiring at the D. C. Department of Human Resources, a mayoral spokesman said yesterday.

The three reports - two by city administrator Julian Dugas and a third from the mayor's Office of Municipal Audit and Inspection - will be the first offical findings from six separate investigations announced in the past seven weeks into alleged irregularities at DHR.

It was these accusations of hiring abuses in DHR, later followed by allegations of contracting and leasing abuses, that led to the mayor's Dec. 3 suspension of his long-time friend and political ally, Joseph P. Yeldell, as DHR director.

The reports are by no means expected to resolve the controversy over Yeldell's stewardship of the city's largest department, however. The reports will only cover allegations that Yeldell improperly used his authority to place friends and relatives as well as political allies of the mayor on the DHR payroll. Hiring and leasing practices will be covered in later reports.

In addition, informed sources said, the auditor's report will not cover the November, 1976, employment of Yeldell's wife, Gladys, as a GS-9 program analyst in the city government's personnel office.

Yeldell and his wife were both interviewed by investigators from the auditor's office. But Mrs. Yeldell's employment is likely to be the subject of a separate auditor's report to be given the mayor in about two weeks, according to sources close to the investigation.

The auditor's report, prepared under the direction of audit office director, David Legge, will make recommendations as to what the mayor should do about the alleged employment abuses. But it could not be immediately known yesterday what form those recommendations would take.

Legge's report originally had been expected two weeks ago. But Legge, saying his efforts had been partially delayed by the Christmas holiday season, was unable to meet that deadline.

Legge said early last Friday that the report was complete and would be given to the mayor later that day. Instead, reporters were told that afternoon that the report would not be presented to the mayor until yesterday and its contents would not be disclosed to reporters until today.

Legge made two visits to the mayor's office yesterday. In the course of the first visit, according to a spokesman for the mayor, "it was learned" that some "supplementary supporting data" had not been included. Legge then returned several hours later and delivered the final version of report to the mayor.

Even though the report was said to have been completed Friday, the spokesman, Sam Eastman, said Legge worked on it over the weekend. Legge would not discuss any details of the report yesterday, including what had been done over the weekend.

Dugas' investigation was the first ordered by mayor. The "first increment" of Dugas' findings was on the mayor's desk on Nov. 23, the day Yeldell was placed on indefinite leave of absence after he defied a directive from the mayor and staged a noon-time support rally.

A second "increment" from Dugas was announced in passing at a Nov. 30 press conference.But the result of both fact-finding reports by Dugas have been dept secret pending the completion of Legge's probe.

The shifting responsibility for the investigations wound up with Legge after several other city officials assigned by the mayor to investigate various alleged DHR abuses became the subjects of similar allegations themselves.

The investigation of alleged nepotism in hiring began Nov. 18 under the directorship of personnel director George R. Harrod. Harrod was replaced by Dugas, however, after it was reported that Harrod also had relatives working for city government.

Dugas was removed from the investigation following reports that he too had had relatives working for the city and, according to sources, had urged Yeldell to sign one of the leases under investigation.

The leasing probe was turned over to the office of the corporation counsel. But after it was reported that that office had approved some of the leases under investigation and its director, Corporation Counsel John R. Risher Jr., had represented one of the persons under investigation in private practice, the mayor gave Legge's office responsibility for all aspects of the DHR probe.

The disclosure of the reports today is expected to be the first of several important developments involving the investigations scheduled for this week.

The D. C. Auditor's office, which is roughly the City Council's equivalent of Legg's office, has begun its own probe of DHR personnel practices. It is expected to present its first report - covering basically the same subject as Legge's report - before the end of the week.

The D. C. Board of Elections and Ethics, which is investigating possible conflicts of interests by Yeldell as a public official, had planned to open a confidential statement of Yeldell's financial interests on Friday.

But, according to informed sources, that opening will probably be postponed because Friday will be celebrated as a holiday (the birthday of Martin Luther King Jr.) by the District government and many offices are expected to be closed.

The two other investigations are under way are one by the D. C. City Council, which is still in its formative stages, and a probe by the U. S. Attorney's Office here of the links between Yeldell and millionaire developer and parking lot magnate Dominic F. Antonnelli Jr.

DHR agreed last year to lease from Antonelli a vacant warehouse and office building at 60 Florida Ave. NE for 20 years at a cost of $5.6 million. Antonellihad purchased the building months earlier for $800,000.