The Los Angeles Police said today that they had identified a man they believe killed 10 lone men, most of them homeless, in a series of slayings last year, and that the suspect shot himself to death last October.

Police Chief Daryl Gates said detectives were led to the suspect through records from the coroner's department and ballistic tests after the series of killings ended as abruptly as they had begun.

The suspect, Marcus Nisby, also known as Michael Player, shot himself to death in a Los Angeles motel room Oct. 10, the police said. Mr. Nisby, 26 years old, had a long record of street robberies.

The 10 victims were slain in a 36-day period that began Sept. 4 and ended Oct. 9 with an 11th attack on a man who survived. The victims were all shot without provocation in the early morning hours in and around the Skid Row area. Several were shot in the back of the head and some were attacked as they slept in alleys or on park benches.

An Added Affliction

The murders were an added affliction to the city's large homeless population, estimated at 35,000 to 50,000 people. But social workers said the series of slayings had done little to change the routines and rhythms of a Skid Row district inured to sudden death and violence.

For three days last month the Los Angeles City Council opened its City Hall chambers as an emergency shelter for the homeless, in addition to other facilities, after four homeless people died on the streets in an unusual cold spell.

In another series of killings, the police late last month announced the arrest of Joseph Danks, a 24-year-old drifter, who they said had confessed to killing six homeless men. Five of the victims were stabbed to death in the Koreatown district in the first week in January.

Mr. Danks, from Gaylord, Mich., who the police said had a history of mental problems, pleaded not guilty to six counts of murder and two counts of attempted murder.

At the news conference today, Chief Gates said that Mr. Nisby shot himself one day after the attack Oct. 9 in which the intended victim survived. Mr. Nisby, who had a number of aliases, was linked to the slayings by ballistics evidence, the accounts of witnesses and physical evidence collected in a search, with a warrant, of a relative's residence where Mr. Nisby occasionally stayed, Chief Gates said.

'That Closes This Case'

Bullets fired from the pistol Mr. Nisby used to kill himself were subjected to ballistic tests with several bullets recovered from the slayings, Chief Gates said.

''That closes this case,'' the chief said.

The police said that Mr. Nisby came under suspicion because he had been mentioned as a possible witness to the killing of Rudolfo Roque, the first victim, who was slain Sept. 4. Mr. Roque, 54, was shot as he walked along a sidewalk.

After the killings ended, and after they had failed to find Mr. Nisby for an interview, detectives searched the coroner's records and determined that Mr. Nisby had shot himself to death. The search of a relative's apartment turned up other other evidence linking Mr. Nisby to the slayings, the police said.

A Dislike for 'Bums'

In the case involving Mr. Danks, the District Attorney's office asserted that the Michigan man said in a tape recorded statement that he disliked ''bums'' and ''dirty'' derelicts. His victims were generally stabbed in the back and several of them had been robbed. The District Attorney said that Mr. Danks had arrived in Los Angeles from Michigan last October.

The Los Angeles police are still looking for one person believed to have taken the lives of nearly a score of prostitutes.

The city has a history of killers who prey on transients. Vaughn Orrin Greenwood was convicted of the throat slashings of nine men in 1974 and 1975. Bobby Joe Maxwell was convicted of two of 10 stabbing murders of victims on Skid Row in 1978 and 1979. Norman Bernard pleaded guilty in 1984 to shooting three derelicts.