CHICAGO (AP) _ Eugene Sawyer, new acting mayor of the country's third-largest city, is known for his ability to find votes, and to find jobs for his family.

Sawyer, 54, the longest-serving black member of the City Council, was elected by the council on a 29-19 vote after a long night of wrangling. He succeeds the late Mayor Harold Washington, the city's first black mayor. Washington died of a heart attack last Wednesday.

A soft-spoken former schoolteacher, Sawyer won the respect of other politicians because his middle-class South Side ward was the city's top vote- producer for Democratic Party-endorsed candidates in recent years.

But his career also has been touched by controversy in which opponents have criticized his use of patronage.

The Chicago Sun-Times reported today that Sawyer used his political clout to place 16 relatives and political supporters, including a son, on public payrolls, drawing salaries totaling $542,226 a year. The newspaper did not cite sources.

The Chicago Tribune, also without citing sources, compared Sawyer's patronage practices to those of former Mayor Richard J. Daley, the acknowledged master of Chicago machine politics.

Asked about the articles at a news conference this morning, Sawyer said: ''They weren't all family members. A lot of that information is incorrect.''

Sawyer said his son is no longer working for the city. Of the other relatives, he said, ''They were all qualified for the jobs they were doing.''

Sawyer's brother Charles was fired as acting revenue director by Washington for accepting $2,500 from an FBI informant during an investigation of corruption in the awarding of city contracts. But Eugene Sawyer stood by his brother, who said he had accepted the money as a campaign contribution to Sawyer's re-election fund.

Another brother, Ernest, is the Chicago Transit Authority's deputy drirector of planning and development, and the alderman has benefited by receiving campaign contributions from Arthur J. Smith, who has a CTA contract overseen by Ernest Sawyer.

The CTA has had at least eight Sawyer family members and political operatives at a time on its payroll, the Sun-Times reported.

Bernice Sawyer, 76, who still lives in the four-bedroom house in Greensobor, Ala., where her son Eugene was born, told the Sun-Times he was taught to help out his family.

''I always told them to look out for each other, and that's what Eugene has done,'' she said.

Prior to Sawyer's election, thousands of demonstrators gathered overnight around City Hall, many of them expressing worries that Sawyer would return Chicago to Daley-style government.

Opponents of Sawyer accused him of making deals with Washington foes and of attempting to return the city to old-line machine politics. But Sawyer denied any deals, and promised to carry on Washington's legacy.

Sawyer, who became a ward committeeman in 1969 and alderman two years later, got his first city job with the help of an uncle, working during the summer for the Streets and Sanitation department. Later, he loyally served Mayors Richard Daley, Michael Bilandic and Jane Byrne.

But he was the first black alderman to break with Mrs. Byrne and support Washington for mayor in 1982. He became chairman of the Rules Committee when Washington's forces reorganized City Council in the spring of 1986.

In a Sun-Times questionnaire earlier this year, Sawyer described his worst fault as ''my non-talkative nature and my trusting attitude to all I encounter.''

Reporters asked him to compare his style with that of Washington, who was buried Monday.

''I guess I might be a little bit soft-spoken,'' Sawyer replied, ''(But) I care about the city as he did.''