Air force F-16 fighter jets were scrambled to intercept the private plane as it flew north-west, but were unable to detect any sign of life behind the aircraft windows which had frosted over, suggesting the cabin may have suffered a sudden loss of air pressure.

Mr Stewart, twice a winner of the US Open, was instantly recognisable at golf tournaments around the world because of his distinctive and old-fashioned plus fours. He was a member of this year's victorious US Ryder cup team.

The Learjet 35 took off at about 9am local time yesterday from Orlando, Florida, heading for Dallas, Texas where Mr Stewart, the plane's joint owner, was due to take part in a tournament among the world's best 30 golfers.

But air traffic controllers lost contact with the pilot soon afterwards as it passed over Gainesville, Florida, on the border with Georgia.

After cruising north-west for about four hours across the breadth of the country, apparently on autopilot, the Learjet seems to have run out of fuel and plunged into a swampy part of north-eastern South Dakota, two miles from the small town of Mina.

The frosted windows, noticed by National Guard pilots, added weight to initial speculation that a sudden loss of air pressure may have caused the passengers and crew to lose consciousness from hypoxia, a lack of oxygen in the blood supply to the head.

The twin-engine jet was equipped with an emergency pressurisation system and oxygen masks. It was not known last night whether or not these safety systems had failed to function. Depressurisation at high altitude could prevent passengers from being able to use their masks before passing out from lack of oxygen.

Bill Janklow, South Dakota's governor, confirmed that no one had survived the crash, and said there were no casualties on the ground. The aircraft went down in marshy pasture, well away from the nearest buildings.

Mr Stewart, aged 42, lived with his wife, Tracey, and two children in Orlando. He owned a share in the plane, using it on a time-share basis to move between tournaments.

The other victims were believed to be the Learjet's pilot, the co-pilot, and two executives of Leader Enterprises, a firm of sports agents.

Stewart was matched against Colin Montgomerie in the final singles of the recent Ryder cup and had taken issue with the home crowd who were abusing the Scot. He conceded a putt on the last green which ensured that Montgomerie won, saying that after what had been going on "he doesn't deserve to have to hole it".

Joe Lockhart, a White House spokesman, said that President Clinton had been kept informed about the incident. He said officials from the Federal Aviation Administration were on their way to the crash site.

Mark Baux, a congressional aide who was near the crash site yesterday, said the aircraft had disintegrated totally.