Mayor Marion Barry, already under attack for his selection of a compromise candidate to head the racially troubled D.C. Fire Department, is now being criticized for his selection of five subordinates to assist the new chief.

Barry last week nominated as a compromise candidate Norman Richardson, a black moderate, to be the new police chief. The mayor also named two whites to be assistant chiefs under Richardson and promoted two blacks and another white to the rank of deputy chief.

Barry's choice of assistants is being critized by representatives of both black and white firefighters.

The mayor termed the promotions "a new leadership package" that would "not only maintain and improve the quality for firefighting and fire prevention services this city deserves, but will also make management of this complex and critical department more efficient."

But Theodore Holmes, president of the predominantly black Progressive Firefighters Association, said his group was concerned because for the first time since 1974, both assistant chiefs would be white. "If the fire chief himself was a compromise candidate, what kind of position does that put him in to have two whites under him," Holmes said.

"In the overall numerical count, we've lost one slot. Secondly," Holmes said, "historically, the fire chief has often come from the ranks of the assistant chiefs. I don't know if down the road we aren't eliminating ourselves from the promotional ranks."

William Hoyle, president of the predominantly white union that is the bargaining agent for the city's firefighters, Local 36 of the International Association of Firefighters, said he was concerned not about the assistant chiefs, but about the promotions to deputy chief because both blacks chosen had been lower on a seniority list than more than a dozen whites who were not promoted.

"The deputies' (promotions) left a bitter taste in everybody's mouth," Hoyle said. "They passed over 16 guys . . .I'm sure it was for racial reasons.

"It's a known fact that the department was mostly white in the past. But why should these guys suffer? It is just unfair, because race is being injected."

The two assistant chiefs announced last week are Edward H. Birch, 56, of Crofton, a 29-year veteran of the force who was acting chief following the resignation Dec. 31 of Jefferson W. Lewis, and John P. Devine, 48, of Upper Marlboro, a 26-year veteran who was one of the leading candidates for chief. Devine, an assistant chief who was continued in the post by Barry, will remain in charge of operations. Birch, who had previously been a deputy chief, will replace the soon-to-retire Calvin Watson as assistant chief for staff services.

The three appointed deputy chiefs are Battalion Chiefs Alfonso Torre, 46, of Beltsville, a 24-year veteran; Theodore R. Coleman, 53, of Oxon Hill, a 27-year veteran; and Joseph A. Kitt, 52, of Southeast Washington, a 29-year veteran who was also one of the top contenders for the chief's position. Coleman and Kitt are black.

For years, black firefighters have complained that whites, through seniority in a once-segregated department, have had a lock on the top jobs. The blacks have closely monitored their own representation in the department, especially in the top 43 posts -- chief, two assistant chiefs, six deputy chiefs and 34 battalion chiefs.

Since taking office Jan. 2, 1979, Barry has emphasized the need to intensify affirmative action and place more blacks in top posts. That has disturbed many white firefighters, who have said that changing the longstanding importance of seniority is unfair to whites who have waited years to get to the top of the list.

In choosing Richardson, whose selection must still be confirmed by the City Council, Barry picked a black for the politically sensitive post. He rejected Devine, who had the support of the union but was considered not flexible enough to carry out Barry's affirmative action goals; and Kitt, who was supported by the black group, but unacceptable to the union and considered by some to be too much of an activist in the area of affirmative action.

Hoyle criticized the failure to select Devine, whom he considered most qualified, as a suggestion to white firefighters that the department's top job was reserved for a black. Holmes said that the reluctance to choose Kitt because of his affirmative action activism would discourage blacks from standing up for affirmative action. Richardson has not been associated with the black firefighters group.

While there is now one less black among the two assistant chiefs, Barry's new appointments have made three of the six batallion chiefs black. Previously, there was only one black.