Soaring at an altitude of 10,000 metres (30,000ft), balloonists Bertrand Piccard and Brian Jones are heading over the Caribbean after reaching Mexico on Tuesday.
They aim to fly between Jamaica and Cuba and then out over the Atlantic.
And having crossed the Pacific - the hardest stretch of their route around the world - Mr Piccard says that only bad luck can spoil their plans.
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If easterly winds permit, the balloon should accomplish its world mission by Saturday, at the Mauritanian city of Bir Boghran.
But Mr Piccard and Mr Jones plan to go even further and touch down at the foot of the pyramids in Egypt after crossing North Africa.
"They have six days of fuel left, which is largely sufficient to reach Egypt," an expedition spokesman, Gerard Sermier, said in Geneva.
Record breakers
The Anglo-Swiss crew have already set several records for ariel circumnavigation.
They were the first to cross the Pacific during a non-stop, round-the-world attempt in such a craft, breaking the ballooning distance record in the process.
With the pilots taking turns to navigate, Breitling took six days and 16 hours to cross the Pacific, considered the most perilous stretch of the journey.
"So that little puddle was what they call the Pacific," Brian Jones joked in a conversation with the Geneva control centre.
The distance record has not yet been officially recognised, but the balloon has clocked up more than 31,000km since leaving the Swiss Alps on 1 March.
The current official distance record is 22,910km.
Brave attempts
In case things go wrong, the Breitling pair are equipped with a kit containing parachutes, inflatable dinghies, life jackets, wet suits and food for several days.
They were relieved when rivals Britons Andy Elson and Colin Prescot were plucked from the Pacific Ocean near Japan a week ago after their round-the-world balloon attempt got into difficulties.
The last attempt by British entrepreneur Richard Branson ended in the Pacific off Hawaii in December.
Balloonists set new record
(17 Mar 99 | Great balloon challenge)
Balloonists are go for Mexico
(16 Mar 99 | Great balloon challenge)
Balloonists break distance record
(13 Mar 99 | Great balloon challenge)
Balloonists 'relieved' as rivals ditch safely
(08 Mar 99 | Great balloon challenge)
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International Ballooning Commission
Breitling Orbiter 3
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