At least four women who roamed the streets of a shabby part of Trenton looking for crack cocaine in the middle of the night met a slight soft-spoken young man.

The women offered sex for drugs, the police said yesterday, and because of that they died.

Investigators said they had charged the man, Anthony Balaam, 31, with killing four women after having lured them into drugs-for-sex encounters. The police said that Mr. Balaam, who uses crack, had confessed to the four killings and that he might be implicated in similar cases.

Mr. Balaam was described by a detective who arrested him, Anthony Manzo, as unassuming and polite, ''a 'Yes, Sir, No Sir' kind of person.''

Deputy Police Chief Joe Constance, who has been on the force for 27 years, called Mr. Balaam, 5 feet 5 inches and 150 pounds, ''one of the calmest and coolest murderers I've encountered.''

After his arrest, without incident on Wednesday, Mr. Balaam talked to detectives in polite, measured tones. ''He talked about rage,'' Chief Constance said. ''He talked about power, about his power over the women.''

Investigators said Mr. Balaam would strike bargains with the women, threaten them with a knife in the sexual encounter and strangle them. Three victims were found in vacant lots and the fourth was in a rundown hotel.

The suspect has been charged with murder in the deaths of Karen Denise Patterson, 41, on Oct. 24, 1994; Valentina Cuyler, 29, on March 19, 1995; Connie Hayward, 27, on April 10, 1995, and Debora Ann Walker, 37, last July 29. Ms. Hayward was found dead in the hotel.

The deputy chief said that Mr. Balaam raped another woman on Feb. 16, but that she escaped before he could strangle her. She provided a description of the attacker, and the police soon concluded that Mr. Balaam was the man who had been killing women on the streets in the predawn hours.

Investigators said that they thought that at least one other woman had fled after having encountered Mr. Balaam, and that they hoped that she would come forward. The investigators added that they were conferring with the police in Detroit, where Mr. Balaam lived from July 1995 to last January, to determine whether he might have committed crimes there.

A homicide investigator in Detroit said yesterday that the city had no string of unsolved murders and that the police did not recognize Mr. Balaam's name.

Not much was known about Mr. Balaam. The police said he had been born in Trenton, was unemployed and lived at 421 Stuyvesant Avenue, where he was arrested about 2:30 P.M. Mr. Balaam has a roommate, the police added.

Two killings were near Mr. Balaam's home, Chief Constance said. The body of the last victim, Miss Walker, was found by Mr. Balaam's neighbors.

One of the neighbors said yesterday that she did not know Mr. Balaam, who lived a few doors away.

''Oh, my God,'' the neighbor, Catherine Emerson, of 415 Stuyvesant Avenue, said in a telephone interview when she learned that a murder suspect lived nearby. She said she had no image of him.

Mrs. Emerson said a neighbor telephoned her on the morning of July 29 and said, ''Go look out the back door.'' Mrs. Emerson did so, and she saw a body in a nearby lot.

''I thought it was a little child,'' she said, recalling the small-frame woman who was on the grass with her blue-and-white coveralls pulled down.

Chief Constance said that DNA testing on semen recovered near two bodies had linked Mr. Balaam to the crimes and that the police hoped that further tests would tie him to all four killings and the rape on Feb. 16.

In addition to murder, Mr. Balaam has been charged with robbery and the possession of illegal weapons. He has convictions on minor burglary and drug charges and has refused offers of counsel, the police said.

Mr. Balaam was being held without bail.

Chief Constance spoke with compassion about the kind of women who were slain.

''It's like 'The Night of the Living Dead,' '' he said. ''They will do anything, literally anything, to obtain the drugs.''