A few days before Christmas, the Central Intelligence Agency delivered a chilling message to H. Kenneth Hill, the U.S. ambassador to Bulgaria: Terrorists had targeted him for assassination on New Year's Eve.

The threat was regarded as "specific and credible" -- serious enough to evacuate Hill and his family from the U.S. Embassy in Sofia and secretly fly them to Paris for the holidays. They left on a Balkan Airlines flight Dec. 22.

"The plans involved a variety of guns and grenades, like they were going to storm the embassy," said a source close to the Hill family. Bulgarian security officials beefed up the guard around the building on Stamboliski Boulevard and arrested five people. The suspects had to be released because no incriminating evidence was found when they were picked up. But the New Year arrived without incident. Hill and his wife returned to the embassy Jan. 2.

The suspects were not members of any pro-Iraqi terrorist cell fired up by Baghdad's appeals for a holy war against "imperialist targets." According to a U.S. counterterrorist offical, they were affiliated with Hezbollah, the Iranian-backed Lebanese Shiite movement. Some anti-terrorist experts say they may have been playing out an agenda of their own or perhaps acting as "provocateurs" bent on exacerbating the crisis between the United States and Iraq.

The episode reflects the difficulties that lie ahead for U.S. and allied counterterrorist officials in trying to guard against the worldwide outburst of terrorism that Iraqi President Saddam Hussein has said he would unleash in the event of war. How much is rhetoric? How much is real? What other radical groups and extremists with motives of their own might join in? And if terrorist attacks take place, what kind of retaliation will follow?

"I am afraid that things are going to happen which will make a deep ditch between the Arab Islamic world and the West," says Hans-Joseph Horchem, a former director of the West German domestic intelligence service who is now head of the Institute for Terrorism Research near Bonn. "What is going to happen is warfare between different cultures and different religions."

Security officials and executives of U.S. defense contractors and other large American and European corporations envisioned grave consequences at a recent, highly confidential "Terrorism Roundtable," according to an account obtained by The Washington Post.

Should war break out, the officials expect anti-American rioting in Jordan, Pakistan, Israel's occupied territories, Algeria, Tunisia, Morocco, Sudan, Yemen and Mauritania. They said they were especially worried about the "ferocity" of such outbursts in Jordan and Pakistan.

The executives also envisioned a wave of Iraqi-sponsored terrorism in Europe, the Middle East, the Indian subcontinent and southeast Asia and said attacks could also come in Latin America, Africa and the United States. The prime targets, they feel, would be U.S. government facilities, commercial aviation and, possibly, private American schools and prominent U.S. corporations.

Potential trouble spots, the security directors said, would include five European cities where Palestinian terrorists have operated in the past: Athens, Brussels, Rome, Vienna and Istanbul. Other areas of concern: Karachi and Manila in Asia and Lima, Santiago and Montevideo in Latin America.

The businessmen said there is a "high" likelihood that Palestinian terrorists allied with Saddam would attempt some attacks in the United States, possibly within five or six days of the beginning of a war.

These, the security directors predicted, would probably be designed to get the most publicity for the least risk, perhaps a bombing in an airport lobby or some other public place. They listed New York, Washington, Los Angeles, Chicago and Detroit as the likeliest locales for such an attack.

The State Department voiced some of these same concerns Friday in a travel advisory warning that increased tensions due to Iraq's failure to withdraw from Kuwait "may lead to demonstrations, terrorist attacks and other hostile actions" against U.S. government facilities and citizens in the Middle East, South Asia and North Africa. Should armed hostilities occur in the Persian Gulf, the department said, "this threat will be heightened."

Some specialists in terrorism, however, are more dubious about the prospects for attacks in the United States and about the scope and timing of Iraqi-sponsored violence abroad.

Robert H. Kupperman, a senior adviser at the Washington-based Center for Strategic and International Studies, said Israeli as well as U.S. facilities in Europe and the Middle East are the most likely targets, but doubted that Saddam would resort to terrorism right away.

"My own guess is he will wait," Kupperman said. "I think it would be a poor use of his terrorist resources to engage them immediately." He said he thought Saddam would definitely call them into play "if we end up going to war and the war turns out terribly badly" for him.

A former senior CIA official, who asked not to be identified, said the threat of terrorism "is an enormous part of Saddam Hussein's psychological warfare," but he said does not think "we are going to find the world blowing up."

He said the CIA's monitoring of international terrorism and its liaison with foreign intelligence services have been "extraordinarily good" in recent years. Other experts agreed, pointing out that outside of the Middle East, terrorist groups now face much more chance of detection than they did in the "easy environment" of the 1970s.

Today, even the CIA and the Soviet KGB share terrorist information. And as the Bulgarian episode involving Ambassador Hill suggests, Arab terrorist organizations can no longer depend as they once did on the support of Eastern European intelligence services.

The question of what Iraqi-initiated terrorism can be expected is really a question about Saddam himself, according to Brian Jenkins, a longtime specialist in political violence and senior managing director of Kroll Associates, an international investigative firm based in Los Angeles.

"Will he, in the event of war, fight that war with an eye to postwar survival?" Jenkins asked. "Or will he instead decide, as Samson in the temple, to use everything he has at his command -- the missiles, the chemical weapons, the biological weapons, terrorism, sabotage -- basically an Armageddon defense?"

Another problem in assessing the terrorist threat is the amount of "noise" that has been made since the Aug. 2 invasion of Kuwait. Terrorist groups are always planning or talking about operations, but they have been doing so in recent months in front of the news media.

"There is always a certain volume of threats, intelligence reports and alarms," Jenkins said. "To a certain extent, the harder you listen, the more you hear. Since August, we've been listening very, very hard so we hear a lot."

In contrast to all the noise, there has been a remarkable dearth of international terrorist activity in recent months. To some U.S. officials, the lull "shows the importance of state sponsorship" for terrorist groups.

"It shows how these organizations are not free-standing," said one State Department anti-terrorist official. "They depend on financing, support and so forth, from governments. Here is a case where the sponsor said, 'Do everything in preparation, but don't get operational.' "

The State Department said last Monday that it was "seriously concerned" about the dangers. It said there have been repeated examples of planning for terrorist activity, such as "suspicious people" hanging around the apartments of U.S. diplomats and cars with occupants using videotape cameras repeatedly driving by their embassies.

Horchem, who said he gets his information from German and foreign intelligence services, said he thinks Iraqi-sponsored terrorists are more likely to go after civilian targets -- such as an urban transportation system or airport -- rather than well-protected U.S. facilities and officials.

Since the invasion of Kuwait, he added, Western intelligence services estimate that about 100 members of terrorist organizations with ties to Iraq have arrived in Europe with forged or stolen passports, "mainly Egyptian and Tunisian." He said many are "support troops," but he estimated that about 30 are "really well-trained and able to handle explosives" like the bomb in the radio cassette player that blew up Pan Am Flight 103 over Lockerbie, Scotland, in December 1988.

Discussing the situation in the United States, Neil Gallagher, FBI counterintelligence section chief, said at a Dec. 10 press briefing at George Washington University: "Historically, Iraqi intelligence officers have been able to operate in the United States, but that capability has been reduced with the reduction in {Iraqi} embassy personnel. The real threat lies with Palestinian rejectionist groups."

Others think the dangers here, as distinct from Europe, are rather remote. "It takes a tremendous logistical chain" from the Middle East to undertake an operation here, said Billie H. Vincent, an aviation security expert. "The Iraqis are not supermen. Terrorists are not supermen. There is just so much they can do."

Special correspondent Jessica Portner, staff writer Molly Moore and staff researcher Ralph Gaillard Jr. contributed to this report.