The Armed Islamic Group is the principal Muslim underground organization waging war against the Algerian government. If the group or its sympathizers are involved in trying to export terrorism to the United States, as U.S. prosecutors suggest, it would mark a radical departure from the group's focus on Algeria.

Until now, France has been the only country that has been victimized by exported Algerian terrorism. France is the former colonial power in Algeria and was strongly identified with the military-backed Algerian government opposed by Islamic militants. Lethal subway bombings in Paris in 1995 and '96 were traced to Algerian terrorists and to the Armed Islamic Group, which is known by its French acronym GIA.

Otherwise, Algeria's eight-year struggle with radical Islamic forces has been internal. Although Algerian terrorist groups are suspected of having received training and material assistance from various radical Islamic states and from veterans of the fight against the Soviet army in Afghanistan, the links have never been solidly established.

The rhetoric of the GIA and other insurrectionist armies in Algeria, as well as of peaceful Islamic political groups, has been extraordinary in the Muslim world for generally ignoring the United States. The demonization of the United States, which is a part of much militant pan-Islamic rhetoric, has been largely absent from Algeria's nationalist rhetoric -- as has any suggestion that the terrorist war in Algeria and France might be exported to North America.

Terrorism has been a fact of life in Algeria since 1992, when a legal Islamic political party, the Islamic Salvation Front, was allowed to participate in parliamentary elections. It won the first round, so the secular, military-backed government canceled the second round, touching off a terrorist war between Muslim militias and the government. Over the past eight years, at least 100,000 people are believed to have been killed, many of them victims of hackings and throat-slittings.

Horrible as the war has been, it has been largely confined within Algeria. Although some of their members may have fought in Afghanistan alongside the anti-Soviet mujahedeen, the focus of the GIA and other radical Muslim groups has been on toppling the military and business elites that have ruled Algeria since the end of its war for independence in 1962.

The prosecution of Lucia Garofalo, arrested last week trying to enter Vermont from Canada, and Ahmed Ressam, arrested this month trying to carry explosives into the state of Washington from Canada, may confound the current analysis. U.S. prosecutors say both Garofalo and Ressam have links to the GIA.

Nevertheless, experts on Algeria and Muslim terrorism doubt that Algerians linked to overseas terrorist activities are agents of radical Islamic groups in Algeria.

According to independent analysts, scholars and diplomats, Ressam, Garofalo and others fit another profile: that of independent holy warriors serving a militant, pan-Islamic cause that is anti-American. Often they are called "Afghans" because they trained in the mountains of Afghanistan and Pakistan during the war against invading Soviet forces in the 1980s. From there they have gone on to join other radical Islamic causes, fighting alongside Muslims in Bosnia and in the southern Russian regions of Chechnya and Dagestan.

Ressam's roommate in Montreal, Karim Said Atmani, fits that description -- an "Afghan" who fought in Bosnia. Garofalo reportedly approached Atmani to provide forged passports.

Atmani, Ressam and their associates were last noticed by counterterrorism authorities in the mid-1990s, as part of an Islamic gang in grim, low-income housing projects near the city of Lille, in northeastern France. A series of armed robberies there that ended in a 1996 firefight between Algerians and French security police revealed the existence of radical Islamic financing operations in Europe as well as the presence among Algerian and Moroccan immigrants of white urban youths, some of them converts to Islam or otherwise inspired by the cause. Garofalo, a Canadian citizen married to an Algerian, might fall in that category as well.

The Vermont arrests led to Geneva and a little-known group of theologically conservative and politically radical intellectuals called the Algerian Islamic League. Among the League's leaders were, or are, Mourad Dhina and Anwar Haddam, both Algerian nuclear physicists.

One question is whether the chain of evidence leads through these European patrons to Saudi businessman Osama bin Laden, who is accused by the United States of plotting the U.S. embassy bombings in Kenya and Tanzania in 1998.

The people currently under U.S. investigation are essentially mules, "people who will do stupid things like carry nitroglycerin across the American border," said Roland Jacquard, a terrorism expert and author who heads the International Terrorism Observatory in Paris. "You can only ask that of simpletons, or someone who's been brainwashed, or whose family has been threatened."

To such extremists from Algeria or anywhere else in the Muslim world, the emergence of bin Laden has provided a new source of motivation. To them, analysts say, bin Laden is glamorous and brave for taking on the United States and wealthy enough to finance his operations.

Young operatives, who may or may not include those arrested at the U.S. border, might be undertaking terrorist actions at the behest of intermediaries working for bin Laden. But, experts said, it is equally plausible that they have no bin Laden connection but want to attract his attention.