It turns out the fatal Brussels attack probably wasn’t the work of a European fascist, nor a Hezbollah hit on former employees of Israel’s defense establishment.

A swift investigation by the Belgian and French security services – or perhaps it was more luck than carefully planned police work – led them over the weekend to the suspected perpetrator of the May 24 attack on the Jewish Museum of Belgium: A young French Muslim, a veteran of a jihadi group fighting to topple the Assad regime in Syria.

Israel received its first briefing on the investigative breakthrough on Sunday. The defense establishment is convinced that this suspect is indeed the man who killed three people, including an Israeli couple, and left one still fighting for life.

But it seems the operational experience he gained in Syria assisted the suspect, Mehdi Nemmouche, only in planning his attack on the unguarded museum in downtown Brussels, not in planning his safe return back to France. Had he been aware that customs agents systematically check for smuggled drugs on buses from Holland to France, perhaps he would have managed to escape instead of being arrested in Marseille. In any event, it’s hard to believe that someone who operated so sloppily would have been capable of discovering in advance that his two Israeli victims once worked for the defense establishment.

Nemmouche’s background is very similar to that of the perpetrator of Europe’s last major anti-Semitic attack, Mohammed Merah, who murdered seven people in a series of attacks in Toulouse, including one on a Jewish school. Merah, who was killed in March 2012, had been trained at a terrorist camp in the Middle East, though it remains unclear whether it was in Yemen or Egypt.

Since then, the civil war in Syria has escalated dramatically, and Western intelligence services believe that more than 1,200 European and North American Muslims are fighting there at any given moment, in an effort to topple the regime. Many are fighting in the ranks of organizations affiliated with Al-Qaida, and some return home afterward to continue their jihad.

Terrorism investigators in the West say that Western Muslims who join jihadi terror groups generally go through four stages: Growing religiosity; a personal or economic crisis that the young man attributes to discrimination against Muslims; ideological radicalization under the influence of a local preacher; and, finally, enlistment in a terror organization in either central Asia or the Middle East. That’s what happened in the past in Afghanistan and Iraq, and that’s what is happening now in Syria, the current principal theater of jihadi operations.

This process runs like a scarlet thread among the terrorists who perpetrated huge attacks in Madrid and London during the previous decade. When these young men return to the West, they seek out new targets to attack: Crowded public places, sites affiliated with the United States and Israel, or Jewish centers. For them, solidarity with the Palestinian struggle is integrated into the larger war against the West.

Western intelligence services know the route young European Muslims take to join the war in Syria (most simply fly to Turkey and then cross the border into Syria, either on foot or by car). But aside from tightening surveillance of preachers identified as extremists, they have not yet found any real way to deal with the problem. Israel can help only on the margins, by sharing intelligence and giving advice on protecting Jewish sites in Europe.

Young men like Nemmouche and Merah have a much greater ability to cause casualties and damage than do the vast majority of hate crimes committed by European Muslims against European Jews. Most of these crimes involve throwing firebombs at synagogues, vandalizing gravestones in Jewish cemeteries, or assaulting their victims with weapons such as knives.

But from the standpoint of Western countries, this is just the beginning of a more serious problem. For almost a year now, American and European intelligence services have worried over the possibility of veterans from the Syrian fighting seeking to perpetrate a mass terror attack like that of 9/11 upon returning home.