Is it a ship? Is it a floating country? Or just the jet set's favourite tax dodge?

Fed up with your pad in Monte Carlo and beach home in Barbados? Maybe it's time to try an apartment that travels the world.

Last Wednesday, a group of around 40 very wealthy individuals gathered for lunch at the Dorchester Hotel on London's Park Lane. Amongst those invited to a slap-up meal by international property agents FPD Savills were ship owners, media barons, property tycoons, industrial movers and shakers and even a couple of members of European royalty. The purpose of the gathering was to tickle their interest in some highly exclusive square footage.

Up for grabs, at prices ranging from pounds 1.5-pounds 5m, was a range of luxurious, furnished apartments each comprising spacious living and dining areas, including two or three bedrooms with en suite bathrooms, fully-equipped kitchens, and a terrace with optional jet pool. Naturally, advanced audio and video equipment came as standard.

As they puffed on their post-prandial cigars, the potential purchasers might well have pondered on which of the four interior design concepts they preferred. Would they plump for Nina Campbell's Traditional Comfort look with its warm colour schemes and cosy furnishings? Or would they go for the Continental look dreamed up by Juan Pablo Molyneux, which combines tasteful antiques with sumptuous fabrics? Then again, there was always the Contemporary look featuring Italian warmth and charisma, not to mention a Maritime design capturing the essence of coastal living and the seafaring spirit.

Yes, there was much to chew on. But what made these as yet unbuilt apartments truly remarkable was not their luxurious fittings but their future location. For they are not to be situated in Barbados or Monte Carlo or any of the other places where the super-rich might normally choose to surround themselves with jet pools and sumptuous fabrics. Instead, they are to be built on a 40,000-tonne ship. What the luncheon guests were being asked to buy into was a revolutionary new concept: the ocean-going luxury resort.

When The World of ResidenSea sets sail in December 2001, the owners of its 110 apartments will be able to enjoy the kind of amenities associated with the world's most exclusive holiday destinations: fine dining, concerts by international artistes, a top-notch health spa, you name it. But they will also be able to enjoy these amenities while constantly travelling to exotic locations and exciting events all over the world. The itinerary for the first two years includes trips to the South Seas, Alaska, the Falklands and China, not to mention visits to the Cannes Film Festival, the carnival in Rio and the Monaco Grand Prix. The ship's slogan? "Travel the world without leaving home."

"It takes a bit of getting your mind round," says Charles Weston-Baker, head of international residential sales at Savills. Certainly, the concept of buying a flat on an ocean-going liner seems an unusual one, to say the least, but in fact it is a logical extension of a growing trend in the cruise industry. Over the past decade, world cruises lasting three or four months have become increasingly popular and one of the upshots of this has been a tendency for passengers to begin treating their cabins very much like their own property, hanging paintings on the walls, and filling them with bric-a-brac purchased at different ports of call. Some even leave their possessions to be stored on the ship ready for their next trip, so that when they return they find their cabins exactly as they left them. Just as if they owned them, in fact. It was while he was mulling over this interesting phenomenon back in 1995 that a lightbulb lit up above the head of a Norwegian called Knut Kloster Jr. His father, Knut Sr, had been one of the pioneers of the modern cruise industry, setting up the Norwegian Caribbean Line in 1966, and Knut Jr had followed him into the family business, ending up heading Norwegian Cruise Line, Royal Cruise Line and Royal Viking Line. Now he saw his chance to pioneer something for himself and to build an apartment ship on which passengers' accommodation really was their home. And so ResidenSea was born, a limited company registered in the Bahamas, with the majority of its backers drawn from the Norwegian shipping and cruise industries.

Kloster's initial plan was to build an 86,000-tonne vessel, bigger than the QE2, with 250 apartments at a cost of $690m, but the project was scuppered at the beginning of last year when the financial crisis in Asia and the fall in oil prices sent venture capitalists scurrying for cover. The new, revised plan is for a ship half the size and about a third of the price, coming in at $262m. Construction formally began on 29 September in Rissa, near Trondheim.

So far, 46 of the ship's 110 apartments have been sold and Weston-Baker is confident that the remainder will have been snapped up by the end of next year. "There are an awful lot of very, very wealthy people," he points out. The target buyer is a successful businessman aged around 50 who already has a few different homes around the world. He probably owns his own company but does not need to be in his office every day. In any case, the ship's state-of-the-art communications facilities mean that he will be able to carry on his work effectively, should he so choose, from anywhere in the world.

But wealth alone is no guarantee of securing a place on The World of ResidenSea. "We don't want any criminals or drug smugglers," says Weston- Baker. ResidenSea's spokesman, Bryn Freberg, goes further. Not only do they not want cocaine barons and Russian mobsters, he says, they do want "people of a certain character and a certain standard - nice people". Freberg says that ResidenSea is keen to avoid "people that absolutely don't fit in or can destroy the atmosphere that we want to create". Potentially disruptive individuals should take note that even if they manage to slip through the net, the residents' committee, together with the ship's captain and its owners, have the power to sell their property and kick them off the ship at a later date if they so choose.

It has been suggested that one of the ship's attractions is its possible status as a tax haven, but as far as British tax law is concerned, even if you stayed on board for an entire tax year it is unlikely you would avoid tax in this country. ResidenSea are keen to point out that they are not marketing the project as a tax-avoidance scheme and in any case most purchasers plan to spend only around four to five months of the year onboard in a series of long and short breaks.

So far, 40 per cent of sales have been in the US, with the majority of the rest being in Britain and Scandinavia. Fourteen have been sold in Britain and Weston-Baker confirms that all 14 purchasers were "very, very nice". While not mentioning names, he says their number includes some celebrities and some royalty. Everyone involved is tight-lipped when it comes to the identities of those who have actually bought apartments and so far the only purchaser to have broken cover is the property developer Peter Beckwith, father of "It girl" Tamara.

One recent report suggested that Roger Moore and Madonna had shown an interest. When I mentioned this to Freberg, he was naturally unwilling either to confirm or deny this, but it is fair to say that he appeared considerably more enthusiastic about Moore than Madonna. "I think he would add something to the ship," he said brightly of the former Bond star, but when asked about the erstwhile bad girl of pop, he sighed: "I wouldn't know".

With its complement of super-rich citizens on board, together with whatever precious valuables they choose to bring, it is possible to see The World of ResidenSea as a potential target for the world's pirates, currently experiencing as much of a boom as the cruise industry. But Freberg is confident the ship is secure. "It demands a lot of resources to attack a ship like that," he says. "And there are easier ways to get to rich people." He maintains that the security on board will be tighter than on any other passenger ship in the world.

And the future? The ResidenSea business plan is based upon the construction of two more similar ships. According to the company's CEO, Fredy Dellis, they expect to begin moving on the second one towards the end of next year. But in the next few months the company will also begin looking at longer-term projects and deciding whether their customer base can be broadened with "something smaller and more accessible", as Dellis puts it. Could this mean broom cupboards for the great unwashed? Time will tell. Maybe one day it won't just be the super-rich who can travel the world without leaving home.