The wounds suffered by the man who led police on a 10-mile Beltway chase Tuesday are prompting authorities to investigate whether he may have killed himself during an exchange of gunfire with Fairfax County police.

In describing the incident to relatives of Merachew Lucas Fitigu, Prince George's County police said the 24-year-old son of an Ethiopian diplomat was struck by two bullets, one of which hit him in the shoulder and a second of which passed through his head, family members said.

Fairfax police, who had pursued the Alexandria resident from Virginia after he fled their speed trap, said they fired as they approached his black Trans Am, which was in flames after striking a guardrail just north of the Temple Hill Road overpass in Prince George's.

Fitigu's relatives said a Prince George's detective told them yesterday that autopsy results would determine whether the head wound was self-inflicted or whether one bullet caused both wounds.

"It is a very strange story," said Tesfa Girmai, 48, a cousin. "The most unbelievable part is they shot after the car was immobilized. He couldn't go anywhere, and they shot him. Why?"

Prince George's police, who are investigating the case because Fitigu died in their jurisdiction, declined to comment. "We just don't have all the facts yet," said Royce D. Holloway, a police spokesman. "We're not going to release any details until the investigation is complete."

But Fairfax police yesterday filled in some details of the chase.

They said their pursuit of Fitigu began about 11:35 a.m. when he passed through a radar speed trap at the intersection of Hayfield Road and Spring Faire Court, in the Kingstowne area of the county. The officer operating the radar, who has not been named by police, turned onto Hayfield Road to stop Fitigu's car, but Fitigu did not pull over when the officer turned on his emergency lights.

The pursuit headed north on Van Dorn Street and reached the Capital Beltway, police said. Fairfax Police Chief J. Thomas Manger said other officers then joined the chase, which was being monitored by a police lieutenant in the field.

As the Trans Am approached the Woodrow Wilson Bridge, however, the lieutenant faced a decision on whether to authorize the pursuit to continue into Maryland. Fairfax pursuit policy states that officers may pursue into Maryland only if they believe a felony or an escape has occurred.

But before a decision could be made, Fitigu fired shots at his pursuers, police said, piercing the fiberglass shell above the front grill of a patrol car driven by Fairfax patrol officer Jeffrey K. Rockenbaugh. Manger said that if the bullet had been several inches higher, Rockenbaugh could have been wounded or killed.

The pursuing officers did not fire at the Trans Am while the chase was in progress, Manger said.

"Only in the most rare and extreme circumstances would we do that," Manger said.

Moments later, Fitigu lost control of his car on the Beltway in Prince George's County. It struck a guardrail, ricocheted back into traffic and hit the guardrail again before coming to a stop and bursting into flames.

Investigators have released few details about what happened next. But Fairfax police said in a statement yesterday that Rockenbaugh--the officer whose car was hit by a bullet--approached the Trans Am and shot Fitigu in the upper body. They refused to say how many shots he fired or what led him to pull the trigger.

Prince George's police said they found a semiautomatic handgun, 1.75 pounds of marijuana and more than $1,000 in cash in the car. They also said they are interviewing several witnesses, including several Prince George's firefighters who were responding to an unrelated call in nearby Oxon Hill.

The firefighters, based at the Morningside station, were driving on the inner loop of the Beltway when they saw the burning Trans Am and stopped to investigate. But before they could get out of their truck, a supervisor on the scene, Battalion Chief Kirk Jackson, heard two gunshots and immediately ordered the crew to take cover, said a fire department spokesman, Lt. Mark Brady.

Brady said the firefighters did not witness the shooting itself. He said they later helped to extinguish the flames that had engulfed the Trans Am.

Fairfax police refused to say how many officers were involved in the chase, although they said three officers, including Rockenbaugh, were placed on administrative leave with pay. Rockenbaugh, 33, joined the Fairfax department in 1989. Police would not name the other two officers, saying they were not directly involved in the shooting.

In the meantime, grieving family members and friends gathered yesterday at the Fairfax County town house of Fitigu's mother, where wails could be heard through an open window. Fitigu's mother was too distraught to talk about her son, known as Lucas, said his aunt, Tsigereda Seyoum.

"There is no talking--just a silent cry," Seyoum said. "Something you've known since birth is just gone."

Family members said Fitigu was born in Ethiopia and spent his early childhood in Italy, where his father, Fitigu Tadesse, was the Ethiopian ambassador.

Relatives said the father now works for the United Nations' Hunger Project and lives in New York. He is separated from his wife. Family members were trying to reach him yesterday to tell him that his son is dead.

Staff writer Tom Jackman contributed to this report.