The Breitling Orbiter 3 balloon is expected to cross the finishing line of 9.27 degrees longitude at midday today, making it the first non-stop balloon flight around the world.
Early yesterday morning they beat the endurance record of 17 days, 18 hours and 25 minutes set by the Cable & Wireless team, which was forced to land off the coast of Japan two weeks ago.
It was the latest in a long line of failed attempts to circumnavigate the globe. This time, the prize is pounds 700,000.
Brian Jones, from Wiltshire, and Bertrand Piccard, the grandson of Jacques Piccard, who took a submarine down to the deepest point of the globe, were yesterday speeding across the Atlantic at speeds of up to 82 knots and were expected to reach the north African coast at 9am today.
A spokeswoman for the project said the two men were feeling focused and upbeat. "They said they were very excited about crossing the finishing line but they won't make a decision about whether they will land in Mali or Egypt until after they have crossed it."
They would prefer to land in Egypt, as Mali has more difficult terrain, she added.
Brian Smith, the air traffic controller for the balloon, said: "We're feeling like horses that can smell their stable."
By 3.30pm yesterday, the men had flown a total of 24,679 miles since taking off on 1 March from Chateau d'Oex in Switzerland. Although the flight has been without any noticeable setbacks, it has taken its toll on the pilots, who are said to have had problems sleeping and to be totally exhausted.
Mr Piccard, a former psychiatrist from Switzerland, used hypnosis to boost his spirits. "It seemed to work for him," said Alan Noble, the team's flight director.
They were also given a major advantage before setting off: permission to fly over China. After Richard Branson strayed into Chinese air space during his fourth attempt to beat the challenge, the Chinese authorities refused to allow any British balloonists to fly over. The Cable & Wireless team was forced to fly around.
The Breitling Orbiter 3 team is Swiss-registered.
The possibility that it mightbreak the record was greeted with good grace by Mr Branson, the businessman who has made several high-profile attempts at the challenge.
He said yesterday that he was unlikely to try again. He had been planning a fifth attempt from Argentina next month, but instead was now hoping to organise a transglobal balloon race.Reuse content