C oleman Young, three-term mayor of Detroit, president of the U.S. Conference of Mayors and one of the most respected black leaders on the national political stage, is in some trouble here at home.

Young has been subpoenaed by a federal grand jury and refused to testify on constitutional grounds. His private town house phone has been wiretapped by federal investigators, yielding an estimated 1,500 reels of electronic tape. And he has not complied with a subpoena for records from a newly combative city council.

Despite all this, Young remains the unchallenged leader of Detroit, the first black mayor in an increasingly black city. He has strongly denied any wrongdoing, lashing out at his critics at home and assailing the city's white-owned newspapers for printing "leaks and lies."

One grand jury here is expected to complete its work in weeks. The grand jury is investigating whether a minority firm owned by a black friend of Young's served as a "front" for several white businessmen to win a city contract to haul sludge. The panel also is looking into allegations that Young's sewer director received kickbacks to keep quiet about the scheme.

A second grand jury probe is focusing on whether another minority firm, headed by a former Washington, D.C., businessman, overcharged the city hundreds of thousands of dollars on a contract to provide bus fuel. That probe also is examining a million-dollar loan that Young's office arranged for the firm.

Young, 64, said he is confident that he will emerge with his reputation intact, but his administration is likely to remain under political siege for some time.

"I don't think for a minute that I'm not a target," Young said in an interview. "I don't know who will be indicted and who won't. There are rumors every week. But there are no official statements about who's a target and who's not, only leaks.

"People have been tried and hung and found guilty in the press. You read stuff in the paper and it's attributed to some goddam Deep Throat. It's put me on the defensive. It's got to have a negative effect."

In his typically blunt fashion, Young also suggested that Reagan administration prosecutors are singling out black politicians for harassment. "These guys have become a Gestapo," he said. "They're misusing the grand jury system."

The mayor's counteroffensive has not gone unheeded. In December, four white city council members voted to enforce their subpoena for the mayor's records, and five black members voted against it.

All this amounts to an enormous test for Young, a former auto worker and Democrat who took office here in 1974. After pushing through unpopular tax increases to rescue Detroit from bankruptcy, he again faces a mounting budget deficit. After helping to create the Renaissance Center, he has watched the downtown complex slide into default. And after scaring off any serious opposition to his 1981 reelection, Young wonders aloud whether this might be his last term.

The allegations being studied by the first grand jury have been recounted in court testimony, accounts in the Detroit Free Press and interviews with knowledgeable sources:

In 1979, a federal judge named Young as special administrator for a mismanaged sewage treatment plant that was polluting the Detroit River. Two white-owned companies, Michigan Disposal and Wolverine Disposal, already had contracts to haul dried sludge from the plant to a nearby landfill. Young said the city needed another firm as a backup.

The mayor's office proposed in 1980 to hire a minority firm called Vista Disposal, but the city council refused because of questions about who owned the company. Nevertheless, Young soon used his special powers to bypass the council and approve a $6 million contract for Vista. Young said this was a competitive process, but local newspapers found that no other bidders were identified.

Vista's owner was not listed on its original incorporation papers, but it turned out to be Darralyn Bowers, a prominent black real estate agent and a close friend and political supporter of the mayor. Witnesses in Bowers' divorce trial later alleged Vista had no employes and no equipment, and investigators began to look into who was hauling Vista's sludge.

They found that some work had been performed by a firm that was a joint venture between Vista and one of the white firms, Wolverine Disposal. They placed phone wiretaps on the mayor's town house and on Bowers' office and home, monitoring conversations involving Young, Bowers, a white sludge company executive and Charles Beckham, the mayor's sewer director.

The grand jury also is investigating allegations that Beckham accepted $8,000 in kickbacks to keep silent about the scheme after he found out about it. Beckham, who could not be reached for comment, has in the past strongly denied the allegations.

In October, Young wrote the U.S. attorney's office that he was declining on constitutional grounds to respond to a subpoena to appear before the grand jury. The mayor did agree to hand over his tax returns.

Bowers said she is Vista's sole owner and that she did not disclose her ownership initially only because of her pending divorce. She said she hires mainly minority truckers and joined with white businessmen only for some initial construction work. She said she knows nothing about alleged kickbacks and had no reason to pay any city official. Bowers added that prosecutors are conducting "a vendetta" against her company and that "maybe they're just trying to get blacks out of the [sludge] plant. Maybe we're just supposed to raise the shovels and dig the ditches." Ronald Zuckerman, a lawyer for Michigan Disposal, would say only that the firm's president has been named as a target of the probe. An attorney for Wolverine declined comment.

Young said he never believed Vista to be a minority front and that he thinks the probe was prompted by complaints from white contractors. "It takes on a certain racial aspect," he said. "There's never been a black company hauling sludge. These were white members of the council against the first blacks who ever received a contract for oil or to haul sludge.

"It's a little bit more than coincidental that the Justice Department is investigating Democratic mayors all across the country," he added. Justice Department spokesman Thomas P. DeCair called Young's assertion "preposterous," saying the agency's investigations are nonpartisan.

The second investigation involves a contract to provide fuel for the city's aging buses. Instead of the city buying that fuel directly, the mayor's office convinced the council in 1981 to contract with a black-owned middleman firm, Magnum Oil Co., as the city's supplier.

Last May, the council's auditor reported that Magnum officials failed to follow a "deescalator" clause in their contract, which was supposed to tie their charges to the market price for oil. Although oil prices had dropped sharply, Magnum Oil continued to charge Detroit more for fuel than any other major city was paying.

The auditor said the company had overcharged the city by $247,000 in eight months, and that projected overcharges could reach $800,000 a year. This was big news in a city whose money-losing bus system had just raised the fare from 75 cents to $1. If that wasn't enough, the council soon discovered that the mayor's office had granted a $1 million loan to Magnum Oil at below-market interest rates. Council members complained that this was done by slipping some fine print into a routine budget item.

Magnum Oil's president, James L. Denson, did not respond to requests for comment. Denson resigned as president of the D.C. Chamber of Commerce in 1980 after allegations that thousands of dollars in chamber funds had been misappropriated. He denied at the time that he did anything intentionally illegal. Magnum's treasurer, S. Allen Early Jr., a well-known black attorney in Detroit and a political supporter of Young's, also did not return phone calls.

Young said the $1 million was simply a prepayment for future oil deliveries. His aides, however, could not show the council any legal authority for the loan. The mayor acknowledged at the time that his office had made "screw ups almost beyond compare," but he would not release any of the contract documents.

When the council subpoenaed the records, Young refused to comply, saying that a state law prevents him from surrendering the records until the grand jury investigation is over. As the council prepared to go to court to enforce the subpoena, the mayor's defenders launched a fierce lobbying campaign. An influential group of black Baptist pastors threatened to mount a recall campaign against any legislator who supported the subpoena. The greatest pressure was brought on black council member Clyde Cleveland, who finally voted against his own subpoena resolution, giving the mayor a 5-to-4 victory.

"The mayor has kind of put himself above everyone else," complained Cleveland, who said he may support a new subpoena effort.

"The mayor has been tremendously arrogant about this, and he's been racist in his rhetoric," said councilman Mel Ravitz, a white liberal. "The feeling among some blacks is that if the mayor's a rascal, at least he's our rascal. But the more the mayor stonewalls, the more people wonder why he is withholding documents and not allowing his department heads to testify." Nevertheless, Ravitz says, "If Coleman Young were to run today, he'd be reelected handily. There's no black candidate that could take him on."