Swedish racing driver Ronnie Peterson died here yesterday of complications following surgery for multiple fractures he suffered in a 10-car crash at the start of Sunday's Italian Grand Prix in nearby Monza. He was 34.

Mr. Peterson had undergone a six-hour operation at Niguarda Hospital here to repair extensive fractures of both legs. He lapsed into a deep coma following surgery and was pronounced dead at 4 a.m. EDT.

In addition to the multiple compound leg fractures, Mr. Peterson had a broken right arm, a crushed right heel and minor burns.

His Lotus and the McLaren of James Hunt of Britain collided shortly after the start of the race at a stretch of the track that had been narrowed.

Mr. Peterson's car ran into the guard rail, caught fire and was hit from behind by the Surtees of veteran driver Vittorio Brambilla. The Italian's skull was fractured and he is being treated at the hospital in which Mr. Peterson died.

Swiss driver Clay Regazzoni blamed the crash on cars surging forward from the rear of the starting grid (Mr. Peterson had qualified fifth among 24 drivers, placing him in the second row). The surge became even more hazardous because of the narrowing of the track, Regazzoni said.

Racing and civil officials have begun inquiries into the accident.

Few drivers escaped as many accidents as Mr. Peterson. A score of topline drivers have died in the past 10 years, but during his 12 years racing the blond Swede survived about 30 accidents and ended up in a hospital only three times.

Mr. Peterson's worst prior accident came in 1969 when he landed upside down in a burning wreck during a Formula Three race at Monthlery, France. He suffered a neck injury and burns on both arms and legs and could not drive for several months.

Born in Orebro, Mr. Peterson was one of the most experienced Grand Prix drivers. Many experts thought he was the fastest of all given the right car.

But in a business so dependent on the equipment, Mr. Peterson got the best cars only two seasons.

In 1971, his first year in Grand Prix racing, Mr. Peterson finished runner-up in a March-Ford to Jackie Stewart in the world championship, althought winning the Europe an Formula Two title that year.With two races to go this year, he was second to world champion and Lotus teammate Mario Andretti.

Mr. Peterson won 10 Grand Prix races, putting him eighth of the list of all-time winners - tied with James Hunt and behind Andretti and Niki Lauda among active drivers - but ahead of men who have become world champions, such as Dennis Hulme and John Surtees.One of his biggest victories was the U.S. Grand Prix in 1973.

The Italian race was his 123rd start in Grand Prix, more than any other current driver. Only the late Graham Hill (176) and Jack Brabham (126) had more GP starts in their careers.

Mr. Peterson switched from March to Lotus in 1973 to join Emerson Fittipaldi, the reigning world champion, and won his first Grand Prix race in France. A strong finish that season, with victories in the Austrian, Italian and U.S. Grand Prix, gave him a third place in the world championship.

In 1974, still with Lotus, Mr. Peterson won three more races but poor results in others put him only in fifth in the driver ranking.

He continued with Lotus for another season but went back to March in 1976 following the failure of the new Lotus to be competitive.

Though his talent often got the March high on the starting grid, the car failed often. Mr. Peterson won that year's Italian Grand Prix, but his only other point-winning performance was a sixth-place finish.

In 1977, Mr. Peterson fulfilled his old dream to drive for Ken Tyrrell. Tyrrell's six-wheeler had shown great promise in 1976, but it was to be a disaster, the car getting less and less competitive during 1977.

But Mr. Peterson picked up seven points from a third, a fourth and a sixth place, and his fights to achieve results with the difficult car were closely watched by the experts.

This year Mr. Peterson rejoined Lotus as No. 2 to Andretti. His was a classic example of team driving, although off the course he admitted he was bothered by being No. 2 and having to give up his best chance at the world championship. He won a thrilling victory in South Africa. But that win, and his subsequent triumph in Austria, were only after Andretti had dropped out.

Mr. Peterson had agreed on a new contract with Lotus that would have made him a co-No. 1 with Andretti next season but, racing sources said, Andretti vetoed the idea. Lotus took on Carlos Reutemann and Mr. Peterson was generally believed to hame reached agreement with McLaren. Mr. Peterson lived outside London with his wife Barbro and their 2-year-old daughter Nina.

The Monza track on which Mr. Peterson was fatally injured has a reputation of being dangerous, and several fatal accidents have occurred on it.

The worst was in 1961 when German driver Wolfgang von Trips ran into the crowd after a collision with another car, killing 15 spectators. Von Trips also was fatally injured.

"I know all the dangers in this game," Mr. Peterson said in a recent interview. "We all do. But you can't think about it when you're driving. Then you're finished."