LONDON — Doctors treating Michael Schumacher for the brain injuries he sustained in a skiing accident in the French Alps said on Tuesday that there was "a slight improvement" in his condition after an overnight operation. But they said the 44-year-old former grand prix driver, the most successful in the century-long history of the sport, remained in critical condition, with extensive blood clots in his brain that were inaccessible to further surgery.

The two-hour operation at a hospital in the French city of Grenoble, the second surgical procedure since Schumacher's accident on Sunday, was undertaken to remove a large hematoma, or blood clot, on the left outer side of his brain, the opposite side to Sunday's surgery, the doctors said.

The second operation, begun at 10 p.m. on Monday, had achieved "a relatively good result," they said, removing the hematoma and somewhat lowering the pressures within Schumacher's brain, leaving him in a "relatively stable" condition.

But Dr. Jean-Francois Payen, a member of the surgical team, said that Schumacher, a seven-time winner of the world drivers' championship in Formula One, remained in a critical condition. It could be days or weeks, he said, if Schumacher survives, before any assessment could be made as to whether he had suffered any permanent brain damage when he skied at high speed into a rock on a snowfield at the resort of Méribel, close to the Swiss and Italian borders with France.

"We can't say he is out of danger," Dr. Payen said, "but we have gained a bit of time."

The French doctor, an anesthesiologist, said that "the coming hours are still critical" for Schumacher, and that the remaining hematomas, described as being widely spread through his brain and too deep to be reached by surgery, meant that it was impossible for the medical team to predict any outcome for Schumacher.

"Things can change very quickly, in a bad way or a good way," he said.

At a news conference at the Grenoble University Hospital Center, the medical team said the decision to operate a second time, following the emergency operation to relieve pressure on his brain as soon as Schumacher arrived at the hospital by helicopter about 90 minutes after his accident, had been had undertaken with the consent of his family.

Schumacher's wife, Corinna, and his two teenage children, Gina-Maria, 16, and Mick, 14, have been at his bedside since the hours immediately after the accident.

Many in the racing world turned to the question, ironic as many saw it, of how Schumacher could suffer such serious head injuries while engaging in one of his family pastimes after surviving a career spanning 21 years in Formula One, a sport where speeds of 200 miles an hour are common. His most serious racing injury was a broken leg sustained in a crash in his Ferrari in 1999.

One account, on the front page of The Times of London, was that Schumacher, whose 45th birthday falls on Friday, would have had to have been skiing at between 60 and 100 kilometers an hour — equivalent to 37 to 62 miles an hour — when he struck the rock. The account quoted unnamed sources at Grenoble as saying the fact that his helmet split on impact indicated that he would have had to be traveling at very high speed, a conclusion that appeared to gain support from the medical team at Grenoble, who described the impact with the rock as having been "very violent."

Resort officials at Méribel said Schumacher, who has a chalet nearby, had been skiing with his son in an off-trail area between two of the resort's main ski runs when he fell and struck his head on a rock. On Sunday, these officials said, the snowfall in parts of the snowfield was unusually shallow, with some of larger rocks covered with a thin dusting of snow that could have deceived Schumacher.

At Tuesday's news conference, doctors said Schumacher would remain in a medically induced coma — a common treatment in cases of severe head injury — for the immediate future and possibly much longer, with hour-by-hour assessments of the degree to which the swelling of the brain was receding.

Some of Schumacher's rivals from his Formula One years said that they considered it unsurprising that he would have chosen a style of skiing that emphasized speed, daring and agility. As a driver, Schumacher was known for his aggressive, win-at-all-costs style, and had a history of on- and off-track confrontations with other drivers.

Apart from the 1999 accident that broke his leg, he emerged unscathed from several other high-speed crashes. In this, he was a beneficiary, like other drivers, from the vastly improved safety measures in Formula One, many of them adopted after the fatal accident involving the Brazilian driver Ayrton Senna at the Imola track in Italy in May 1994.

Schumacher, then challenging Senna for supremacy in the sport, was running immediately behind Senna when the Brazilian veered off the track.

There has been no fatality in Formula One since.