Research and design teams at Dassault in France and Gulfstream in New York have been told they must have their designs in the air by 2015, when Concorde is expected to be "retired".
The Anglo-French airliner, introduced in 1976 as the last word in aviation technology, is starting to show its age. Last weekend, flights between London and New York were cancelled because of technical problems, and despite a consistent demand for seats from business travellers, no replacement supersonic airliner has been commissioned. Unless an alternative is found in time, harried executives will no longer cross the Atlantic in 3hrs 50mins - around half the time taken by a conventional plane.
And in an age when time is money, the commercial potential for aerospace companies is clearly considerable. Dassault and Gulfstream are using advanced design technology to put together plans for a mini-supersonic jet, able to carry a dozen or so passengers at 1,300 to 1,500 mph through the stratosphere.
Engineers on Dassault's Falcon SST project say only that there are still many technological difficulties to overcome. Their American rivals, working on an aircraft code-named SSBJ, are more tight-lipped.
Until recently, supersonic travel was thought too expensive to be commercially viable. But a surge in demand for executive jets during the Nineties has led manufacturers to rethink. Owning or hiring a business jet is increasingly seen by companies as an essential method of transporting staff around the world.
Analysts believe orders for 580 corporate jets at pounds 2m-plus apiece will be placed worldwide this year, compared with only 353 in 1996. In Britain alone, at least 300 jets are owned by companies, while a decade ago there was only a handful.
So great is the demand that Airbus and Boeing vie to supply business versions of their passenger jets. Boeing's A319, with 124 seats, has been bought by firms such as Daimler/Chrysler who ferry staff between the US and Germany.
In the Eighties no executive jet was complete without gold taps and ample storage for the champagne. Now the emphasis is on technology without trimmings. The latest business jet interiors look more like a mid-range BMW or Mercedes, with leather seats and walnut veneer, than a Bentley.
From a standing start three years ago, "fractional ownerships", in which companies buy a share in a jet, have attracted at least 50 European firms, the majority in Britain. This figure is expected to double next year.
For pounds 400,000, they can purchase a one-eighth share in a jet and a helicopter for short trips around Britain. Then, with four hours notice, they can use the plane whenever they need.
One of the newest fractional ownership brokers is Sunseeker Superyachts, set up in March. "Airlines are merging and companies are doing away with frequent flyer fares," said Nick Davis, their director of aviation. "If you are a computer firm, and a customer with a multi-million pound contract has technical problems, your support team can be sent out so much quicker in a business jet. In the early Nineties, firms were doing away with planes but now they are seen as a business tool. It is easier for companies to justify a jet if it is for the whole company's use, not just fat-cat directors."
Graham Forbes, of the General Aviation and Manufacturers and Traders' Association, said corporate jets offer security and accessibility. "On a scheduled plane you've always got someone looking at your work, which is not the case on a business jet," he added.
Some fractional ownership companies have already declared an interest in supersonic business jets. Graeme Deary is sales director for NetJet, a European subsidiary of the world's largest fractional ownership company, which is owned by the American billionaire Warren Buffett.
"As soon as the jets are rolling off the production line, we will put in an order for 50," he said.
HOW MAN HAS SHRUNK THE ATLANTIC
1492: Christopher Columbus: Canaries to Bahamas, one month.
1620: Pilgrim Fathers: Plymouth to Cape Cod, two months.
1919: Alcock and Brown fly west to east in 16hrs 27 min.
1927: Charles Lindbergh makes first solo Atlantic flight in 331/2 hrs.
1934: Queen Mary crosses Atlantic in four days.
1939: Pan American Airways runs first commercial transatlantic airline service.
1974: Lockheed SR-71A "Blackbird" crosses in less than two hours.
1976: Concorde: first supersonic passenger crossing, 3hrs 50min.Reuse content