IN APRIL, when the United States bombed Libya and most of Europe crossed to the other side of the street, the Atlantic alliance looked to be entering a period of unprecedented strain. At the Tokyo summit, however, almost all was smiles. There is a temptation to conclude that Europe's and America's differences on combating terrorism were swept under a rug, but something better happened, and not just during the Tokyo interlude but earlier, in the weeks following the April rift.

In those weeks, the United States made headway in communicating two messages to Europe. It provided the "direct, precise and irrefutable" evidence of Libyan complicity that enabled and propelled Europeans to understand why President Reagan had acted and why he had to act. It also conveyed -- and here American public opinion, forming on a separate track, reinforced the official view -- that for Americans a basic alliance transaction was involved. The message was not simply that the Europeans would have to be more supportive in order to keep a determined United States from being more unilateral. It was that the premise of common interest on which the United States assists in the defense of Europe was being undermined by Europe's reluctance to help the United States in its pursuit of interests in areas outside Europe where the Atlantic powers customarily do not act as an alliance.

The result was that before the summit the Europeans took some specific steps to tighten up their policy -- expelling Libyans, and so forth. At the summit they joined the United States in an expression of common purpose that does not ensure united action or (administration claims notwithstanding) isolate Col. Qaddafi; but it does enlarge the area of consensus in which discussion of future steps can begin. The Tokyo statement on terrorism is not self-enforcing. Europe has not suddenly put its Third World policy in American hands. But the statement indicates a satisfying if modest new readiness on the part of the Europeans and Japan and Canada to move away from a strictly national point of view. Washington returned the favor by refraining from demanding more from the allies than the political traffic could bear.

Since the Libya raid, the allies have calmed down, and the United States has itself, while pressing for a collective approach, acted with care. In the Arab world only Libya's few current friends have rallied around; most Arabs have kept their distance in their fashion. The Palestinian problem remains a principal source as well as pretext of much Middle East terrorism, and it must be tended to, for reasons extending much beyond considerations of terrorism. Still, the Palestinian issue is not being used as widely as it earlier was to justify passivity in the face of terrorism. More bombs will go off, but more will be done against the bombers, across a broad spectrum of policies and in more of an alliance context too.