How nations support terrorist operations around the world. As the US seeks Europe's support for a retaliatory strike on Libya, Europe is asking for proof of Libyan sponsorship of bombings in Greece and West Berlin. Details in these cases are still unclear. But much is known about the channels nations use to support terrorism.

In the aftermath of last December's attacks at the Rome and Vienna airports by Palestinian gunmen, police discovered that one of the terrorists was carrying a Tunisian passport. In itself, that was not strange -- except that the passport in question had been confiscated by Libyan authorities last August from a Tunisian worker expelled from Libya. The implication: Libya provided the false documentation that helped the Abu Nidal group carry out the attacks.

That example, according to Fran,cois Le Mouel, head of antiterrorist operations for France's National Police, is an exception proving the rule. Usually, he says, it is much more difficult to find evidence of state support for specific terrorist operations.

How else do nations support terrorist operations? Over the last several decades, enough information has come to the surface to allow Western intelligence analysts to draw some fairly firm conclusions:

Money. It is one of the easiest forms of support. Libya is a prime example: Muammar Qaddafi, whose nation reaps substantial amounts from its oil industry, is known to have supplied millions of dollars to Palestinian, Latin American, and European terrorist groups.

The USSR, too, is known to funnel vast quantities of funds through Eastern Europe and such other clients as Syria, South Yemen, North Korea, Cuba, and Nicaragua.

Some of the money that supported the 1983 bombings of the US and French military headquarters in Beirut reportedly came from Iran, passed to the terrorists by Iran's ambassador to Syria, Ali Akbar Mohtashami.

Sometimes the money comes as a form of pay-off from nations which, while not directly sponsoring a terrorist organization, wish to protect themselves from attack. According to Israeli intelligence sources, Saudi Arabia provided $150 million a year to the Palestinian Liberation Organization, until the PLO was driven from Lebanon in 1982. Now, these sources say, the figure is $30 million to $40 million.

How is the money used? Some Mideast terrorist leaders are known to lead elegant lives -- staying at the finest hotels, living in villas in North Africa, and traveling at will. But the money also flows in dozens of more mundane ways. According to Israeli sources, Syria paid an Arab student in Rome $1,000 to provide details on the layout and schedule of the El Al airline office there, presumably in preparation for an attack.

Training. Nations sponsoring terrorism also provide training in such areas as weaponry, explosives, methods of assassination, paramilitary tactics, intelligence gathering and analysis, and ideology. Numerous camps exist in Syria, Syrian-controlled eastern Lebanon, and Libya for training Palestinian terrorists.

A report on state-sponsored terrorism prepared last summer for the Senate Judiciary Committee noted that some 2,000 terrorists from 20 countries had been trained in Qom, Iran, and that camps in Nicaragua staffed by Cuban, Libyan, and PLO personnel aid terrorists throughout Latin America.

The report also noted that members of the Basque terrorist group ETA in Spain and of the Red Army Faction in Germany have trained in camps in South Yemen run by the Popular Front for the Liberation of Palestine, and that members of the illegal Irish Republican Army in Northern Ireland had been trained in Libya.

There are also widespread reports of terrorists receiving training in the USSR and East European countries.

Support from embassies and safe houses. Nicaragua, for example, is said to be playing host to terrorists belonging the PLO, the Montoneros from Argentina, the Baader-Meinhof Gang from West Germany, and as many as 44 members of the Italian Red Brigades.

Once outside these countries, however, terrorists need places to hide and communication contacts. State sponsors often provide these through diplomatic facilities, in direct contravention to international law. The terrorists who hijacked an Air France jet from Vienna to Tehran in August 1983 are thought to have stayed in the Iranian Embassy before leaving for the airport.

After a British policewoman was killed by gunfire from the Libyan ``people's bureau'' in London in 1984, police found weapons stored in the bureau -- all of which had come in via the so-called diplomatic pouch.

Weapons. Money supplied to terrorist organizations allows them ready access to the Middle East arms markets -- where, according to Western arms-watchers, you can even buy a tank if you have the cash.

But state sponsors also provide arms directly. When the Cyprus-registered steamer Claudia was captured by the Irish military off the coast of Ireland in 1973, it was carrying 5 tons of weapons from Libya to IRA terrorists -- part of an IRA-Libyan deal reportedly worth $1 million and involving 100 tons of arms. Most of the weapons were of Soviet-bloc manufacture.

Terrorists of Italy's Red Brigades have also received arms from the Soviets, via Soviet-supported PLO groups in Lebanon, according to the Senate report.

State sponsors provide support in other ways, too:

Intelligence. Bulgarian intelligence officials apparently had a hand in supporting the Red Brigades in the kidnapping of US Brig. Gen. James Dozier in 1981 in Italy. Syrian intelligence played a major part in the truck-bombing of the United States Marines in Lebanon.

Space for facilities. The PLO maintains its headquarters in Tunisia, a major office in Moscow, and a radio station in Baghdad. Also, Israeli sources say, several thousand guerrillas loyal to Yasser Arafat are encamped in western Iraq, not far from Jordan.

Moral support. Libya, both by playing host to meetings and conferences among terrorist organizations and by the statements of Colonel Qaddafi, provides significant encouragement for terrorism.