THE CAPTURE of Abdullah Ocalan, head of the Kurdish separatist and terrorist party known as the PKK, gave Turkey the chance to show it could run a transparent and reasonably fair trial. In the eyes of the United States and the Council of Europe, the Turks did this passably well in the course of convicting Mr. Ocalan and giving him a death sentence that is now under review. But a second, larger challenge remains -- to make a political deal between Turks and the great majority among the 12 million Kurds (a fifth of the population) who support nonviolence.

The Turkish establishment has a strategy: to neutralize the PKK not only as a military threat but as a political actor and to look elsewhere among the Kurds for interlocutors at once moderate and representative. But many in the armed forces as well as in civilian life in Turkey are more eager to isolate the PKK than to look for Kurds to build up in its place. President Suleyman Demirel set an example by meeting elected Kurdish mayors, but too many Turks lack his view of the big picture. Turkey cannot expect to bring peaceful Kurds into a dialogue if it is not prepared to permit them certain cultural and then political rights.

The PKK Kurds, defeated in battle, have been alert to the emerging requirement to make themselves an acceptable political partner. From his jail, Mr. Ocalan has called for a cease-fire, a "show of goodwill" and a reconciliation with the state. In their most conciliatory gesture in 15 years of war, dozens of PKK guerrillas the other day offered to turn themselves in. At this point, however, the Turks are unwilling to take the PKK's professed abandonment of insurgency to heart. Ankara is playing the amnesty card stingily.

It matters to the United States that Turkey's window of political opportunity remain open. Turkey is a friend, ally and economic and strategic partner. But, to its anger, the United States and Europe, though sympathetic to its terrorist threat, have hesitated to accept Turkey as a political equal as long as it was commiting terrible human rights abuses against Kurds. Here lies Turkey's chance for a breakthrough with its Kurds. Here lies the United States' duty to encourage Turkey along its difficult way.