THE TWO-PRONGED terrorist attack in Kenya on Thursday, probably by al Qaeda, extends the network's recent strategy of spreading the war to American allies and unexpected locales. In recent months, German, French, Australian and now Israeli citizens have been singled out for murder because of their countries' alliance with the United States; Tunisia, Indonesia and now Kenya have been chosen for their susceptibility to penetration. The nature of the targeting is an indication that the war on terrorism has deeply impaired al Qaeda's ability to strike directly at the United States or on the territory of its major allies. Yet the scale and sophistication of the latest attack, in which a suicide bombing against a resort hotel nearly coincided with an attempt to shoot down an Israeli airliner, demonstrates that the enemy remains formidable, well-directed and well-supplied. At least 13 innocent people, including two Israeli children and a number of Kenyan entertainers, died Thursday; but a far greater tragedy was averted only by the fact that the missiles fired at the passenger plane missed.

The logic of the terrorists is transparent enough: They seem to hope that by targeting U.S. allies they can weaken the anti-terror coalition and that by murdering Israelis they can add to the Arab following of Osama bin Laden. Chances are they are wrong on both counts. Australians, like Germans or French, might have had reason to wonder after 9/11 whether al Qaeda was really a threat to their countries; now they can have no doubt. Similarly, Palestinians, like Indonesians or Tunisians, understand that they can only be damaged by association with al Qaeda; polls show that a majority in the West Bank and Gaza now oppose terrorism by their own militants -- not to mention those Saudis or Somalis who would act in their name.

Some argue that the quickening pace of al Qaeda attacks means that the United States cannot afford to marshal its forces and allies for other battles, such as a campaign against Iraq. Yet the Kenya episode offers the latest evidence that the terrorists won't be stopped by military forces -- there is simply no way to guard every resort in the world frequented by Westerners, or every airport served by Western airlines. The battle against al Qaeda primarily must involve intelligence, police work and financial controls that can break down its network -- and an unflinching assault on the sources of Arab and Islamic extremism, wherever they might be found.