Now the island's internationally recognised Greek Cypriot government wants the European Union to keep its promise and open talks on making Cyprus a full EU member. Germany and other countries argue that the EU would be mad to absorb a dispute as bitter and complicated as that in Cyprus.
Just as EU foreign ministers sit down over lunch in Brussels to thrash out what to do, word arrives that four Greek Cypriots have been killed along the Green Line dividing government-held southern Cyprus from the Turkish-occupied north. The government, backed by Greece, retaliates by vowing to take delivery within a week of a batch of Russian S-300 anti- aircraft missiles ordered in January 1997.
As a Russian-Greek naval convoy carrying the warheads and launchers edges towards the eastern Mediterranean, the Turkish armed forces swing into action. Troop reinforcements pour into northern Cyprus. Planes raid the Greek-built missile base near Paphos in south-western Cyprus. The Turkish navy prepares to blockade the island.
Greece declares Turkey's actions a cause for war and, angry at lukewarm EU support, invokes the secret defence clause of a recently signed treaty with Russia. Fighting on Cyprus spreads to disputed Aegean islands on Turkey's coastline.
The United States warns Russia not to get involved. President Alexander Lebed, with Chinese support, tells the US to mind its own business.
All three powers go on nuclear alert. Like Cuba, another island involved in a missile dispute 36 years before, Cyprus has brought the world to nuclear confrontation.
If the above scenario seems fantastic, bear in mind that much of it is already unfolding. First of all, the EU gave a cast-iron promise in 1995 to open accession talks with Cyprus, even though with hindsight some states regard the pledge as rash. "Anyone who wants to join the EU must know that the European Union cannot deal with the accession of new members that bring in additional external problems," Germany's foreign minister, Klaus Kinkel, said last Monday.
This is to lock the stable door after the horse has bolted. Knowing that EU membership talks must start by about mid-1998, and encouraged by Greece, the Greek Cypriots feel they can play hard to get on a Cyprus settlement. Without major Turkish concessions, they will demand that southern Cyprus joins the EU on its own - a sure recipe for a crisis.
Secondly, President Glafcos Clerides and Rauf Denktash, the Greek Cypriot and Turkish Cypriot leaders, may meet in spring to launch fresh peace talks. But even if such talks get under way - a big if - there is little reason to suppose they will be crowned with success. The diplomatic climate is too frosty, and both sides have a deeply entrenched belief that to blink first will be to lose.
Thirdly, several clashes along the Green Line erupted last year, causing the deaths of four Greek Cypriots and one Turkish Cypriot. It was the most violent period on the island since the Turkish army's invasion in July 1974.
Lastly, the Cyprus government says that the missiles it ordered from Russia will cost 200m Cyprus pounds (pounds 250m) and will arrive in 16 months - May 1998. According to a government spokesman, Yiannakis Cassoulides, the deal does not include a clause allowing Cyprus to cancel the order.
Turkey says that its armed forces will attack the Greek Cypriots if they deploy the missiles, whose range enables them to destroy planes in mainland Turkish airspace. Turkey has also talked of imposing a naval blockade of Cyprus.
According to one Nato diplomat with long experience of Turkey, these are not idle threats. "Turks can be incredibly stubborn in matters where they think the national interest is at stake. They've got to be taken seriously," the diplomat said.
This week Turkish naval vessels are visiting northern Cyprus in a show of teeth-baring solidarity with the Turkish Cypriots. Turkish and Turkish Cypriot forces may also be combined for the first time at a new military base in the north.
For its part, Greece's Socialist government is preparing a huge, 10-year modernisation of its armed forces that will cost 4,000bn drachmas (pounds 9.64bn), or almost pounds 1,000 for every man, woman and child in Greece. Greece has also tightened its military links with the Greek Cypriots, especially by creating a common defence space.
In short, virtually all the ingredients for a bloody confrontation on Cyprus, sucking in Greece and Turkey, are present. The island is the world's most densely militarised confrontation zone. Like a dormant volcano that finally releases a torrent of fire and ash, Cyprus is poised to explode after 22 years of diplomatic stalemate and military stand-off.
All outsiders, from the United States and the EU to the United Nations, recognise the dangers. Indeed, many see Greece and Turkey, whose mutual antagonism long predates their alliance in Nato, as the most likely contestants in Europe's next war.
Some Western experts believe that conflict may break out over other Greek- Turkish tensions, notably the disputed Aegean islands. This issue brought Greece and Turkey close to war in January 1996.
Still, everyone agrees that the status quo on Cyprus is untenable, and that the atmosphere is distinctly more tense now than it was six months ago. UN peacekeepers report more frequent trouble along the buffer zone separating Greek from Turkish Cypriots. But to agree on the problem's nature is not the same as to agree on its solution. The peculiar feature of the Cyprus dispute is that it drags on even though most of the world thinks it knows what a settlement should look like.
In 1991 the UN Security Council adopted Resolution 716, which called for Cyprus to evolve into a "bicommunal and bizonal federation" - that is, a single state comprised of two politically equal communities. Mr Denktash was not impressed. It is hard to believe that he will ever sacrifice his beloved Turkish Cypriot pariah state, set up in 1983 but recognised by no country except Turkey.
There are 30,000 Turkish troops in northern Cyprus, and the region's demography has been transformed by the arrival of large numbers of Turkish Anatolian settlers since 1974. They now make up more than 50,000 of the north's population of 180,000.
All the evidence suggests that Turkey intends to remain in northern Cyprus for the long term. However profound their disagreements on other issues, Turkish leaders of all stripes - nationalist, military, liberal, secular, Islamist - show a remarkable unity of purpose over Cyprus, the so-called "national cause".
The key to a deal therefore lies in Ankara - at least, as long as the world believes that reunification must underpin a lasting settlement on Cyprus. Only Turkey can make the vital concessions that would make a reality of reunification.
It would have to pull out most or all of its occupying army, disband the rogue Turkish Cypriot state, remove Turkish settlers, return Greek Cypriot territory and property, and much else besides. However, there is not the slightest reason to think that Turkey plans to do any of these things.
Worse still, the ability of the US and the EU to persuade Turkey to make concessions has considerably diminished in the past year. Less receptive to US and European advice, Turkey is more inclined than ever to question the benefits of its allegiance to the Western alliance.
This is partly because of frustration with the EU. Turkey introduced several important measures of political liberalisation in late 1995 to secure a customs union with the EU, but Greece has blocked the funds that were to flow to Turkey as a result. Turkey is fed up with European criticism of its human rights record and with those who say it should never be offered full EU membership.
Turkey's alienation from the West has increased since the appointment last June of Necmettin Erbakan as its first Islamist prime minister since the Ottoman Empire's collapse. Much of his foreign policy has amounted to one long calculated snub to the West, particularly the US.
He has found time to visit Iran and Libya, but he has kept clear of Washington and EU capitals. When the US said Turkey should stop threatening to attack the Greek Cypriots, Turkey denounced the advice as "beyond the limits of diplomatic courtesy".
Turkey's relations with the West have rarely been trouble-free, but the recent downturn could hardly have come at a worse time. The Turks feel let down and taken for granted by the West, while the US in particular is increasingly alarmed at the erratic Mr Erbakan.
In such circumstances, suspicions and misunderstandings can only grow - between Turkey and the West, Turkey and Greece, and Turkish and Greek Cypriots. The risk of war will rise, and the scope for pre-emptive diplomacy will shrink, unless the US and Europe make the gathering Greek-Turkish crisis their top priority.
TURKEY ON THE GREEKS
'We strongly hope that Greece and southern Cyprus will give up these intolerable provocations and come to their senses, because the Greeks know our nation very well ... They saw the results of their efforts in 1922 and 1974.'
Necmettin Erbakan, Turkish Prime Minister
'Greece and the Greek Cypriot administration have based their policies against Turkey on a fanatic and hostile mentality, which can be described as an incurable illness.'
General Ismail Hakki Karadayi,
Chief of Turkish General Staff
'If they step on our feet, we in turn will step on both their feet.'
Turhan Tayan, Turkish Defence Minister
GREECE ON THE TURKS
'From 1995, the Turkish armed forces have established as a national interest the changing of borders in the Aegean...They are making military preparations in this direction.'
Akis Tsochadzopoulos, Greek Defence Minister
'Instead of concentrating on internal problems such as the lack of democracy and human rights, the Turkish government has pursued a nationalistic position towards Greece.'
Costas Simitis, Greek Prime Minister
'This visit [by Turkey's Foreign Minister to northern Cyprus] proves that Turkey cannot adjust to international legality...We denounce such actions. We believe they worsen the already bad climate.'
Dimitrios Reppas, Greek government spokesman