LOS ANGELES (AP) _ Gang members seeking reliable transportation apparently killed a college couple to eliminate witnesses to the theft of the couple's car, investigators allege.

Three alleged gang members were arrested Sunday and a fourth was being sought in the slayings of Michelle Anne Boyd, 18, a student at UCLA, and Brian Edward Harris, 20, a student at California State University, Northridge.

The two were abducted Sept. 30 and their bodies were found Sunday in a field a quarter mile west of the San Diego Freeway. Both had been shot in the head, police said.

''The motive that we've obtained so far is that the suspects were out looking for a crime to commit, they were having some problems with their engine, they wanted a more reliable piece of transportation, so they took the kids in that car and executed them,'' police Cmdr. Larry Binkley said. The couple, who were raised in Thousand Oaks and met at a record store where they worked, were abducted outside Miss Boyd's apartment near the UCLA campus. It was her first day at the university.

''They (gang members) were about to commit a crime and they saw the kids walking out to their car and decided to take it,'' Binkley said.

''They were driven from where the kidnapping occurred to the location where they were executed,'' police Lt. Mike Carpenter said.

Harris' car, which had been soaked with gasoline and set afire, was found last Tuesday behind an auto parts store. A fingerprint found inside the vehicle led to one of the suspects.

Deandre Brown, 21, Damon Redmond, 19, and Stanley Davis, 20, were arrested Sunday and booked for investigation of two counts of first-degree murder. One led detectives to the field where the bodies were found, Binkley said.

At least two of the suspects were arrested for investigation of a similar crime in June 1984, after a UCLA student said they abducted him and stole his car, Binkley said. They were not prosecuted, however, because the student's identification was considered inadequate, he said.

Detectives allege the couple were killed to eliminate witnesses.