STATE-SPONSORED TERRORISM. The April 15 strike against Libya by US aircraft called dramatic attention to the growing involvement of states in sponsoring or supporting terrorism. While terrorists do not need help from a government to carry out their activities, the ready availability of money, weapons, safe havens, communications, and public support has made it easier for terrorists to attempt their objectives.

What he remembered later was the way their eyes glittered. And how, when they came into the slanting winter sunlight in the terminal at Rome's Leonardo da Vinci Airport from the automobile ramp outside, they walked unusually close together. There were four of them, wearing long coats and scarfs pulled up nearly to their eyes. Amazing, he thought to himself later, that no one noticed them.

Later he learned they had also been high on drugs.

He was standing at a Trans World Airlines station next to the El Al Israel Airlines counter, waiting for a flight to Washington.

``I turned and saw them,'' recalls the American archaeology professor, a resident of Rome who prefers not to be named. ``Then I turned back and was in conversation with one of the people I was in line with.

``The next thing we knew, we heard the sound of [grenades and] firing, and fortunately my companions and I hit the floor.''

From where he lay, he could see the airport security forces returning fire -- plainclothes men who suddenly produced long-barreled revolvers and, to identify themselves to one another, little paper hats. When it was over, he recalls, ``there were a lot of shell casings on us and around us.'' One of the terrorists was 10 feet away.

The event described took place on the morning of Dec. 27, 1985 -- the date of one of the most chilling incidents of international terrorism in recent years. Within minutes of each other, gunmen hurled grenades and opened fire at El Al counters in Rome and at Vienna's Schwechat Airport. Fourteen bystanders and four terrorists were killed at the two locations.

Who did it, and why?

In the days following, some of the possible motives began to grow clearer. A previously unknown group called the ``Martyrs of Palestine'' said the attacks were in retaliation for the Israeli bombing of the headquarters of the Palestine Liberation Organization (PLO) in Tunisia last October. Western intelligence experts, however, pinned the blame on the notorious Abu Nidal group, a breakaway PLO faction, whose motives may have included a desire to embarrass PLO leader Yasser Arafat.

Whatever the intricacies of motivation, always a complex subject when analyzing the political affairs of the Middle East, one thing soon became clear: These Palestinian gunmen were not acting on their own. Behind their attacks lay a web of state sponsorship involving a number of countries.

Investigation of the airport attacks has revealed:

The two attacks were probably masterminded in Libya, where Abu Nidal is thought to live now. Two days after the incidents, Libya described the operation as ``heroic.''

The attackers made use of several Tunisian passports that had been confiscated from workers expelled from Libya earlier in the year. These passports were then probably turned over to the terrorists by Libyan authorities.

The terrorists were trained in Iran and came to Europe through Syria, according to Italian police intelligence specialists.

The gunmen used AKM assault rifles (a modern version of the Soviet Kalashnikov) manufactured less than a year before they were used and all traceable to the same serial number block from a Romanian factory, according to United States sources. The nature of state support

How significant is state sponsorship -- the organized support of independent terrorist organizations by governments?

That question was put to dozens of government officials, intelligence analysts, police and military officers, and antiterrorism specialists from a number of countries in the last few months. Their answers provide some revealing insights.

State sponsorship is rapidly gaining recognition as a major item -- maybe the major item -- on today's antiterrorism agenda.

``International terrorism,'' Central Intelligence Agency (CIA) Director William J. Casey told a conference at Tufts University in 1985, ``is inconceivable apart from the financial support, military training, and sanctuary provided to terrorists by certain states.''

``Without states, [terrorist] groups couldn't maintain themselves,'' says Prof. Yehezkel Dror of the Hebrew University in Jerusalem. ``They would be unpleasant but not very harmful without state support.''

There is broad agreement that the list of worst offenders includes the Soviet Union and its East European satellites; the three major Middle East players (Iran, Syria, and Libya); and, to a lesser extent, Iraq, North Korea, South Yemen, Cuba, and Nicaragua.

There is, however, substantial divergence of opinion about the relative importance of states that support terrorism. Some European governments tend to play down the Soviet hand, while many US experts see it as significant. Many Europeans, and some Americans, feel that the US has overemphazed Libya's importance and boosted Col. Muammar Qaddaffi's image among Arab nations as a ``Yank-buster.''

Many agree, however, that Middle Eastern sponsorship of terrorism poses the most immediate threat: Of the 184 incidents of terrorism in Western Europe recorded by the US State Department for 1985, about 40 percent were related to Middle East groups or countries.

State sponsorship takes many forms. It may come as direct financial aid, allowing some terrorist leaders to live in posh North African seaside villas, travel to fancy hotels, and even maintain retirement funds.

Other assistance includes training for young recruits in weaponry, explosives, methods of assassination, paramilitary tactics, and intelligence gathering and analysis. These skills, along with ideology, are taught at dozens of camps in Syria, Syrian-controlled eastern Lebanon, Libya, Iran, Nicaragua, and elsewhere.

In addition, states can funnel funds and weapons through their embassies, establish safe houses among sympathizers in various countries, and provide weapons, transportation, intelligence, storage and planning facilities, and moral support. There is even a hierarchy among sponsoring states: ``If you have an address in Moscow and you're a terrorist,'' says British antiterrorism expert Brian Crozier, ``you've arrived, you've made it.''

State sponsorship is difficult to prove, partly because to publicize evidence of links between states and terrorist groups might jeopardize the intelligence agents who gathered the evidence.

``Western governments know much more about international terrorist connections than they pretend to know,'' says a high-level official of the West German government in Bonn, ``and yet they use this information less than they could be expected to.'' Why support terror?

Why do states sponsor terrorism? Most do so because they reap clear benefits in political and foreign policy objectives.

First, terrorism can be cheap: A few thousand dollars spent on what some view as paramilitary activity can sometimes produce far more impact than millions spent in conventional warfare.

``To the degree [states] provide support,'' says Ambassador Edward Marks, a counterterrorism specialist on leave from the State Department, ``they increase exponentially the capability of terrorist groups. Most of them are quite small. And here they are with airplane tickets, and money, and documents, and [rest and recreation] -- all of that because they are getting support from a government.''

Second, fueling conflicts by means of terrorist groups allows sponsoring states to maintain a fa,cade of innocence. In their recently published book ``Terrorism as State-Sponsored Covert Warfare,'' Ray. S. Cline and Yonah Alexander observe, ``What sets apart the use of terrorism from more conventional forms of coercive force at a sovereign state's disposal, is the option of a plausible denial or lack of public accountability.''

Beyond that, answers tend to vary from country to country.

Iran, which US State Department officials describe as ``currently the world's leading supporter of terrorism,'' uses such tactics in its campaign to root out Western ideas from the Middle East and spread Ayatollah Ruhollah Khomeini's own brand of Islamic fundamentalism. Iran strongly supports the 800-member Hizbullah, or ``Party of God,'' operating in Lebanon. As the region's major non-Arab state, Iran also uses terrorism to pursue centuries-old animosities with its Arab neighbors.

Syria, which plays host to such anti-Arafat Palestinian terrorist leaders as George Habbash, Ahmed Jabril, and Abu Musa, has a more secular view. Bordering on Israel (which it despises as an intruder into the region) and Lebanon (parts of which were partitioned off from Greater Syria in 1943 under Lebanon's French mandate), Syria has territorial and political designs on these and other nations. As a Soviet client state, it also acts as a channel for Moscow's interests.

Libya, whose sponsorship of terrorism has attracted the most attention recently, may actually be a less significant player than either Iran or Syria. ``If we look at the total volume of terrorist activity worldwide,'' says the Rand Corporation's Brian Jenkins, ``those actions credited to Libyan sponsorship account for perhaps 3 or 4 percent of the total.''

Colonnel Qaddaffi has been a loud protagonist for terrorism, however, using it in particular as a tool against his Libyan enemies abroad, against Israel, America, and several European countries. At a meeting of 22 radical Arab groups hosted by Qaddaffi in Tripoli last February, the groups vowed to form a ``revolutionary strike force and suicide squads'' to strike at American targets.

At bottom lies Qaddaffi's desire to persuade other Arabs to join in some kind of pan-Arab union -- with, presumably, Qaddaffi himself at the head.

Different though these three motivations are, there is ``quite a lot in common between [these three nations],'' according to University of Aberdeen scholar Paul Wilkinson. Noting that they are all ``bitterly anti-American, anti-Zionist, anti-NATO,'' he says that ``it wouldn't be surprising to find a sort of loose alliance among those states.''

Such an alliance, in fact, may have been operating in the case of the Rome and Vienna massacres.

In the background, a bigger question remains: the role of the Soviets. For the most part, Soviet support for terrorist groups appears to flow through East Germany, Czechoslovakia, Bulgaria, Romania, and Cuba, all of which are active in promoting the destabilization of Western society.

For example, Czechoslovak Maj. Gen. Jan Sejna, one of the highest-ranking Communist officials ever to defect to the West, told interviewers from Tufts University last year that the Czech intelligence service, under the direct control of the Soviets, had ``extensive'' contacts with the Irish Republican Army, had provided substantial funds to the PLO, had developed a plan to terrorize Britain by poisoning the water supply, and had become involved in drug trafficking in Latin America in a conscious effort to use drugs to ``destroy Western societies.''

Miguel Bolanos Hunter, a former high-ranking Sandinista counterintelligence officer, told the same interviewers about the extent of Soviet, Cuban, East German, and Bulgarian involvement with Nicaragua. Speaking of the long-range plan to overthrow Mexico, he noted that ``Ideologically, terror, as opposed to prolonged guerrilla warfare, is not a problem. The people in charge of subversion . . . don't care about blowing up a busload of people if that action will have the desired effect.''

Britain's Lord Chalfont, a noted terrorism expert, comments that ``There's absolutely no doubt that the Soviet Union, through the KGB and its various externalizations of the Kremlin, does clearly manipulate terrorism rather well.''

But the trail is carefully disguised. Former CIA head Stansfield Turner, recalling his days in office, notes that ``I never saw conclusive evidence of any state supporting indiscriminate terrorism -- certainly no evidence that the Soviets train the PLO to go out and do whatever the PLO wanted to do.

``I don't say they don't do it; I'm saying it's circumstantial evidence and very largely inference as far as I've ever seen.''

And as Rand Corporation scholar Paul B. Henze notes, Soviet sponsorship of terrorism is only one part of a larger picture.

``If the Soviets are supporting terrorism to the extent that I think they are,'' he says, ``they don't call it that at all. They call it political operations to advance socialism.

``The context is subversion and destabilization; terrorism is only one aspect.''