DAMASCUS, Syria (AP) _ Today's ''godfather of terrorism'' is sometimes 14 years old.

At that age, Tareq Same said, he joined the Palestinian guerrilla movement. He is now 17 - he sucked hard on his Syrian cigarette - and ready to die.

''I want to do a suicide mission. With an explosives belt,'' the skinny boy in fatigues told a visitor. ''It's my duty.''

His comrades, crowded into a charcoal-heated room above the muddy lanes of the Yarmouk refugee district, said they all knew of someone who carried out suicide attacks against Israeli troops in nearby Lebanon.

And what of attacks on civilians, like the Palestinian slaughter of Americans and others at Rome and Vienna airports last December?

''If the American administration does not stop supporting Israel,'' a young guerrilla shot back, ''we are ready to do operations worse than Rome and Vienna 3/8''

Teen-age bravado, perhaps - but of a dangerous variety.

Like the lone surviving terrorist in the Rome attack, three of Same's companions said they lost family or friends in 1982 when Palestinians at Beirut's Sabra and Chatilla camps were massacred by Israeli-allied Lebanese Christians.

And, like the Rome gunman, they want to strike back, at almost anyone.

Such bitter desperation is bringing the Palestinian movement to a fateful crossroads, said knowledgable Arabs, Israelis and Westerners in the region.

Combined with new political frustrations within the Palestinian leadership, it could turn the guerrillas again toward all-out international terrorism, these diplomats and other specialists said in recent interviews.

The latest split between Jordan and Yasser Arafat's Palestine Liberation Organization, derailing efforts toward an Arab-Israeli peace, has left ''an atmosphere of utter hopelessness,'' among Palestinians, said one West European ambassador in close touch with the PLO.

''Arafat's opponents can now say his policy of moderation was wrong,'' said the diplomat, who granted an interview on condition of anonymity, ''and that terrorism, killing innocents, is the only language Israel and the United States understand.''

Since 1974, ''establishment'' Palestinian guerrilla organizations have sought to distance themselves from terrorist outrages committed by such renegades as Abu Nidal, blamed for the Rome-Vienna attacks. But the larger groups are now feeling pressure.

''If we oppose operations like Rome and Vienna, we will look weak in the eyes of our people,'' said Khaled Abdel Majid, a leader of Same's guerrilla group, the Popular Struggle Front.

The Palestinian guerrilla story, in many ways, is the story of contemporary terrorism.

After King Hussein's army drove the guerrillas from Jordan in 1970, depriving them of a vital base for attacks on Israel, they plunged more deeply into global ''armed struggle.''

They shocked the world with bloody ''spectaculars'' - skyjackings, the Munich Olympics siege, the massacre at Israel's Lod Airport. They became ''godfathers'' of terrorism, training radical groups from Europe and elsewhere.

But in 1974 the PLO, exploring political avenues to peace, declared it would confine future attacks to Israeli territory. Angry hard-liners split off into runaway anti-Arafat bands, such as Abu Nidal's Fatah-Revolutionar y Council.

In 1982, Israel invaded Lebanon and drove the PLO from its base in Beirut. Scattered among a dozen Arab countries, the guerrilla groups quarreled, grew dispirited, became further radicalized.

Israeli terrorism expert Ariel Merari notes parallels between today and the dangerous period after 1970. Without political advances to appease the Palestinian rank-and-file, he says, the PLO leadership may again feel a ''need for spectacular violent activity.''

Tamar Prat, Merari's colleague at Tel Aviv University's Jaffee Institute of Strategic Studies, says the violence is already stepping up.

The number of incidents of Palestinian international terrorism doubled in 1985, to about 70, she reports. She believes it will expand further.

''I think Arafat will continue going with the political process, there will be a split, and the rest will go with the 'armed struggle' option. It will mean more international terrorism,'' she said in a Tel Aviv interview.

Thirty-eight years after they fled Palestine, the refugee nation of 2 million Palestinians, packed into dismal shantytowns in Lebanon, Syria and Jordan, feels time is running out for their dream of regaining a homeland. They are being squeezed from many sides.

The Arab oil slump impoverishes Palestinian camp families that depend on income from relatives working in the Persian Gulf. The U.S. government has reduced contributions to the U.N. agency that supplies food, schooling and other services to Palestinians. In war-battered Lebanon, unemployment has reached 50 percent. And Israel every year tightens its hold on old Palestine.

''Why do you think all these young people risk their lives?'' a prominent Palestinian moderate, Hazem Nuseibeh, asked in an interview in Amman, where he serves as a Jordanian Cabinet minister.

''They risk their lives, sometimes misguidedly, because they are homeless, desperate. They feel they are victims of tremendous injustice.''

The guerrilla groups offer a purpose, comradeship, a little money - often about $300 a month.

By Israeli count, the more than one dozen groups have at least 20,000 guerrillas, about 6,000 based in the Syrian-controlled Bekaa Valley of eastern Lebanon and 3,000 more in Syria itself.

A poor country, Soviet-aligned Syria can offer no direct financial help to the guerrillas, but it serves as a conduit for money from other Arab states and for guerrilla arms purchases, Israelis and U.S. officials said.

It also offers safe havens, such as Yarmouk, on the fringes of this city of French-style boulevards and teeming old bazaars.

Once a Palestinian tent camp, now a slum of 40,000 people jammed into crude two-story concrete homes, Yarmouk provides rest and recreation for young Popular Struggle Front guerrillas on leave from their Bekaa base.

Same and his comrades played chess, read and discussed ''irrhap'' - ''terrorism'' in Arabic - with their visitor.

Told that Abu Nidal's gunmen cut down children in the Rome-Vienna attacks, they expressed surprise.

''I didn't know about innocent victims...,'' 22-year-old Ali Qasem said uneasily. But then bloody memories flooded back.

''There were innocents in Sabra and Chatilla, too 3/8' he said angrily. ''What about that 3/8 Was that a good job?''

NEXT - Part III: Euro-Terrorists