The rare breed, characterised by its unique gold coat and renowned for its beauty, stamina, speed and intelligence, has been produced in this little-known desert nation for more than three millennia, making it one of the oldest horse types in the world - the ancestor of both the Arab racehorse and the English thoroughbred.
Until last year their sale abroad was either strictly controlled or forbidden altogether, so jealously guarded is their bloodline.
About 60 horses will be auctioned next month in Ashkabad, the capital. The dramatic change of policy is the work of Saparmurat Niyazov, Turkmenistan's autocratic leader, who sees the Akhal-Teke as a useful means not just of making money but of raising the international profile of his young, formerly Soviet state.
Prices will start at about $12,000 (pounds 7,500), though some horses may start at $100,000. The event is causing a predictable stir in the horse-trading world. French, English, Irish and American buyers are already said to have expressed interest.
Mr Major was not the only leader to benefit from Mr Niyazov's generosity: King Fahd, Francois Mitterrand and Boris Yeltsin all received a horse, although Mr Yeltsin's is said not to have survived the trip to Moscow.
Mr Major's, on the other hand, is doing well: named Maksat, it was trained by the British Army at Melton Mowbray for ceremonial duties, but was found to be too temperamental and too small to bear the weight of a British guardsman. Although technically the property of the state, Maksat is still registered in Mr Major's name, and is now living it up on a private stud farm in Wales.
It may compete in an endurance competition at novice level next year.
Maksat is one of a handful of Akhal-Teke horses living in the West, most of which were bought from the Soviet authorities before the break-up of the Union.
In Ashkabad even this modest exploitation by Moscow of Turkmenistan's pride remains a source of bitterness. The bloodstock of the breed has been fiercely protected since before Alexander the Great defeated the Parthians in the 4th century BC on an Akhal-Teke named Bucephalus - the only horse that has given its name to a city - although cross-breeding has occurred throughout history. Oliver Cromwell, a great horse-fancier, owned an Akhal-Teke named the Darcy White Turk, thought to be a forefather of the English thoroughbred.
The breed takes its name from Akhal, the name of this region since ancient times, and the Tekke, its original tribal inhabitants. No more than 1,000 pure-breds are now believed to exist worldwide.
Fourteen of them are in Britain and there is a dedicated owners' association run by Sue Waldock, a former hotel- restaurant manager who fell in love with the breed in the early 1980s.
"They're excellent at all sorts of skills, particularly endurance, being desert horses: they're highly intelligent and athletic," she says.
"There's always interest when they appear in public because they look so distinctive."
Next month's auction in Ashkabad is just a small part of a revolution that is taking over the Turkmen horse industry. The country recently joined the International Horsebreeders' Association in Geneva, while a horsebreeders' congress will be held in Ashkabad to coincide with the auction.
The Ashkabad hippodrome, where horse races are held every Sunday, is being modernised. A state-of-the-art loudspeaker system has been installed in the new grandstand and this month trackside gambling will be legalised for the first time.
Annaguly Nurgeldiev, director-general of Turkmenatlary, the state racehorse association, plays down the significance of next month's sale.
"Every business has its financial specifics," he says. "It would be counter- profitable if we didn't sell." He adds that around half the 3,000 Akhaltekinskaya racehorses in existence are already privately owned, and insists that the sale represents no great change in policy.
Mr Nurgeldiev, who has no experience of horses, was appointed to the post last year.
His qualification is as an entrepreneur - from 1992 he ran a private company with interests in road construction and leather processing - and it is clear from the way he speaks that his brief is to modernise the horse-racing industry and steer it towards self-sufficiency. All this is designed to attract foreign interest and investment, which are crucial if Turkmenistan is to succeed in exporting its vast reserves of oil and gas.
The Akhal-Teke is therefore both a tool of capitalism and a potent national symbol: a useful double role that President Niyazov, who calls the breed the "effulgent diamond" of the equine world, is doing his utmost to exploit.
Every banknote of the local manat currency features both the President's face and a racehorse, rampant, as the watermark.
A statue of the President stands at the entrance to the state stud farm (home to his personal mount, the eight-year-old Piadar), along with a banner proclaiming that the love of horse-breeding is a sacred duty for all Turkmen.
Although the auction is unprecedented in modern times, President Niyazov is unlikely to do anything that might jeopardise the value of an asset with which he has specifically linked his country's future.
Only stallions will be sold, and numbers will be carefully limited, while the best horses, the so-called gold stock, will not be on offer.
Next year a Turkmen team will take part in the Nissan World Equestrian Games at Punchestown, in Ireland; they have high hopes of winning the 160km, eight-hour marathon event, and with some reason.
The Turkmen still remember an event in 1935 in which several breeds of Central Asian horses rode from Ashkabad to Moscow, and which was won by an Akhal-Teke.
Sergei Ivanov also won a gold at the 1960 Rome Olympics on an Akhal-Teke named Absent.
A word of warning to prospective buyers, however: these horses are a handful, and are notoriously difficult to train. "They only answer to one master," says Ilmurat Agamuradov, a third-generation trainer and chief breeder at the state stud farm, just south of the city. "They don't much like strangers - even the smell of strangers can make them shy."
Ms Waldock confirms that this is not a beast to put out in a field and ride at the odd weekend: "They respond best to daily love and attention, a bit like a dog," she says. "If you ignore a dog it will misbehave too. Bonding with a human owner is in their blood."
r Interested parties can contact Turkmenatlary on ++(7)3632-478634 / 475916/300985. They will need to speak Russian or Turkmen. Or the .-Teke Society of Great Britain, Bodare Cottage, Daymer Lane, Trebetherick, Cornwall PL27 6SA; 01208-862964.