ANCHORAGE, Alaska (AP) _ Police said Monday they were investigating a possible link between the weekend shooting of a man in his car and an unsolved 1976 car bombing that killed his sister.

Robert Pfeil, 55, an Alaska Airlines pilot for 29 years, was shot at an intersection near his fashionable home. He remained in Providence Hospital under police guard, and his condition improved to serious from critical, police said.

Pfeil was shot Saturday night as he drove home after a flight to Kotzebue and Nome. He was hit at least three time by bullets fired from what was believed to be a .45-caliber weapon, police said.

On Monday, police said they were looking for an older, light-colored sedan that had been seen speeding from his neighborhood after the shooting, and that they had contacted the Alaska State Troopers to aid in the search.

Pfeil's sister, travel agency owner Muriel Pfeil, was killed in downtown Anchorage on Sept. 30, 1976, when her car was demolished in a bomb explosion. The bombing remains unsolved.

Police Chief Brian Porter said he was unsure the two cases were related, ''but we're not taking any chances until we can tell.''

Pfeil's wife, Marianne, said she could think of no reason why someone would want to kill her husband, and added that he had not been pursuing his own investigation into his sister's slaying.