Heard the one about the twins separated at birth who don't meet each other for 52 years? When they do get together, it's embarrassing and difficult to be more than merely polite. Sometimes it works, sometimes both wish they had stayed strangers. That's the story of Eilat and Aqaba, two towns 15 minutes apart that are taking the first halting steps towards getting to know each other.
In any other part of the world, there would be no problem. But this is the Middle East. Eilat is in Israel. Aqaba is in Jordan. Politically, they were a million miles apart.
But they could now be brought together in a way no one would have thought possible a decade back. There's cautious optimism that this could be a reunion to die for - as hundreds of thousands of people have.
Already it is possible to cross the frontier for a double holiday, staying in what is rapidly becoming the Middle Eastern Riviera in Eilat, then moving to Aqaba, a typical Arab town and beach resort with miles of coastline that have never seen even a deckchair.
But it's a bureaucratic mishmash. Traffic is mostly one-way: Israelis going to Jordan. You drive over from the last place where the blue-and-white Star of David flag flies, and go through security and passport control. You next walk 100 yards or so (with your luggage, and generally without trolleys) to be greeted by Jordanian frontier guards who demand your passports and about £20 for a visa. The sum varies. Both sides seem to change their minds about how much they want every time the wind alters direction. One country makes a decision, the other matches it.
Yet all this is set to change and the twins could even become triplets in time, taking in the Egyptian resort of Taba, just across the Red Sea from Aqaba. Taba now consists of little more than an hotel and a casino.
The day I was in Aqaba, talks had begun between Israel and Jordan to allow ferries to cross the five miles or so of Red Sea between the two countries, which the Jordanians and almost everyone else call the Gulf of Aqaba and which Israelis know as the Gulf of Eilat. The idea is that both sides would respect each other's customs and security proce dures. This would also allow cruise ships to visit both places, instead of one or the other, which is what happens now. The ships would anchor at sea and send out tenders to both Aqaba and Eilat simultaneously. You could go back to your ship for lunch and then switch countries.
If Egypt joins the talks, all three nations might agree to do away with the bureaucracy of customs and security.
And it could all happen soon. What might take a little longer is a joint Eilat-Aqaba airport. At present, Eilat airport is in the centre of the town, like an old railway station. It is suitable only for planes from other parts of Israel. To travel to the resort from abroad on one of the twice-weekly El Al or Superstar flights from Heathrow, for instance, you have to use a former military airstrip in the desert 45 minutes away. Aqaba, however, has an underdeveloped airport that already has received Concorde. The plan now is that runways at Aqaba would serve both towns - and both countries. Again, there would be joint customs and immigration facilities, and no visa charges for Britons.
The only snag is that the site of the planned Israeli terminal is in a bird sanctuary and bird watchers represent an important slice of Eilat's tourist market. The project will probably happen anyway.
Holiday development in the area has a lot to do with a London businessman, David Lewis. Tour the Eilat area in one of the glass-bottomed boats that patrol some of the world's most glorious corals and the guide will talk about the way Lewis has revolutionised this, Israel's most southern point.
'We talk about before and after David Lewis,' said Rina Maor, director of the Ministry of Tourism for the area. And it is easy to see why. Unofficially, locals have dubbed part of Eilat 'Lewisville'. He has six hotels catering for all tastes, with another two being built. The luxurious Royal Beach is one of the most elegant resort hotels I have visited. It has three superb swimming pools, vast lounges and, for those on the 'presidential floors', a special lounge with a terrace overlooking a pool. There, snacks are served all day and a bottle of local sparkling wine in an ice bucket is always ready.
Lewis's other hotels range from the five-star King Solomon's Palace to the self-catering Ambassador.
Significantly, Lewis is now building a hotel in Aqaba, too, thanks to a suggestion put to him by a member of the Jordanian royal family at a banquet five years ago on the day the peace treaty between the two countries was signed. That alone seems to show that there is something about the peace process that is working. The Arab town has only 1,000 hotel rooms. Eilat has more than five times that number. Lewis and his son, Simon, are creating an Aqaba hotel that will be virtually self-sufficient, although with regular shuttle links to the town . Of course, Aqaba is no more a place on its own than is Eilat. From the Israeli resort, you can travel to Tel Aviv, Jerusalem or Galilee. Aqaba is the gateway to the Arab world- two hours from Petra, the jewel of Jordan.
You immediately see three countries from the Aqaba beaches, as you can from Eilat. The Israeli hotels look as close as the tower- blocks down the road in an average British suburb. A yard or two further along the horizon is Egypt and once you have driven from the Israeli border it's but a five-minute ride to the Saudi Arabian frontier.
Both towns have ports. Aqaba is the Red Sea outlet to Iraq, with consequences that became apparent during the Gulf war. Both Jordan and Israel are trying to underplay the ports' role and put more emphasis on tourism. Both sets of docks are to be moved to provide a cleaner sweep of beaches,
The Aqaba hotel will be run by his Israeli chain, Isrotel, under a different name, but staffed by Jordanians. Lewis - a 75-year-old former RAF navigator who built up hotels in Spain as well as the River Island clothing empire- doesn't want to be thought to be telling the Jordanians their business. 'I have much too much respect for them to do that,' he says.
Not everyone is enthusiastic. I suggest to Yousef Dalabeeh, president of the Aqaba Regional Authority, that tourism would be one of the principal ways of guaranteeing the peace between the two countries. 'No,' he corrected me. 'That is not the way. First, we must have a real peace that is felt by the people - and that is still dragging behind. Then we can talk about joint tourism.' But I had the feeling that this wasn't a universally held view in Aqaba. The manager of the Radisson-SAS hotel there says: 'Tourism will very definitely help peace.'
The fear is that Aqaba may become a copy of the brightly lit Eilat. Dalabeeh stresses: 'The Aqaba people are different. The culture is different.' The quiet boulevard outside the Radison Hotel wouldn't fit in to Eilat at all. You're as likely to see a camel, escorted by a man in flowing robes and red head-dress, racing down the road as you are a Mercedes.
The Aqaba authorities are very conscious of protecting their environment, which is why the coral reef there is protected by wardens; something the Israelis wish they had done years ago. 'The environment and development are enemies,' Dalabeeh says.
Nevertheless, there is a feeling that the Aqaba tourist industry is envious of Eilat's achievements, particularly such projects as its sophisticated underwater observatory, stretching deep through the coral to provide views of the beautifully coloured fish. There is scuba diving as well as snuba diving, a combination of scuba and snorkel. For £25, you can hire equipment to comb the depths, attached to a line that will haul you up at a moment's notice. Aqaba, however, does have a simpler version.
If you prefer dry land, Eilat has Jeep trips into the desert and camel rides. If Aqaba adopts all these things,too, it might indeed run into the danger of resembling Eilat a little too closely.
But the head of the Eilat Hotel Association, Alon Dekel, says: 'Making the two towns alike would defeat the whole purpose of the two-centre holiday. We want people to visit us both - because we are different."
Eilat is also different from the place it used to be. Blink and there's a new hotel gone up, a new marina installed. When I first went there 27 years ago there were three small hotels, a parade of rundown shops and a few sleazy restaurants. There weren't even any traffic lights. When Lewis first visited it in the early Sixties, he says, it was 'like the Wild West', with one hotel. 'They used to joke,' said Dekel, 'that Israeli judges would send convicts to Eilat when the prisons were full.'
One thing that doesn't change is the weather. Europeans know it as a winter holiday destination, with temperatures approaching 80F at Christmas.
Lewis says: 'I first came here from Tel Aviv where it was grey and wet. I arrived to find blue skies and sunshine - and that was when I decided to build here, in a place that nearly always has blue skies and sunshine.'
If Lewis does bridge the gap between Israel and Jordan with his new hotel he will have performed what would once have seemed a miracle. But, as people used to say in that part of the world, the impossible occurs all the time, miracles take a little longer.
• Michael Freedland was a guest of the Royal Beach Hotel, Eilat, and the Radison SAS Hotel, Aqaba. His El Al flight was organised by Superstar Holidays (tel:0207 952 4300). Bookings for the Royal Beach can be made via Isrotel (Tel: 0208 991 4532).