With Yasser Arafat's demise, there seems to be no end to speculation on the chances of arriving at a peace agreement with his successor or successors. Was Arafat the obstacle to arriving at such an agreement? Was he the only obstacle? Is it going to be possible now that this obstacle has disappeared? It is instructive to look at the history of Israel's efforts to arrive at peace treaties with its Arab neighbors in past years. That history may contain some lessons of value in the future.

After 30 years of hostility punctuated by four wars, Israel and Egypt signed a peace treaty in 1979. That treaty, which established relations of "cold peace" between Israel and Egypt - including as one condition the presence of an Egyptian ambassador in Israel, which has been violated by Egypt for much of that period - has, nevertheless, regulated relations between the two countries for the past 25 years. Fifteen years after Egypt, and only after Israel's agreement with the PLO at Oslo had paved the way, Jordan followed suit in 1994. The agreement with the PLO, intended to be followed by a peace agreement between Israel and the Palestinians, turned out instead to be a prelude to unprecedented bloodletting that continues to this day.

For a treaty to have meaning, the signatories must, obviously, be willing and capable to enforce its terms. Egypt, Jordan, and Israel have done just that. Israel did it by following in the tradition of democratic countries, its government carrying out the obligations it had undertaken on behalf of its citizens. The leadership of Egypt and Jordan enforced the terms of the agreement with Israel by utilizing the state's security services to crush any opposition intent on using violent means to subvert the signed agreements.

Yasser Arafat, the late leader of the PLO, turned out to be unwilling, incapable, or uninterested in suppressing the opposition to the terms of the Oslo Agreement he had signed with the late Yitzhak Rabin. Rabin, who had hoped that Arafat - unencumbered by civil rights organizations and judicial oversights - would crush Palestinian terrorist organizations intent on continuing terrorist acts against Israelis, was to be disappointed, and the agreement failed to meet its promise.

Dealing effectively with the opposition of Palestinian terrorist groups has been recognized by President Bush in his "road map for peace" as the essential element needed to permit progress toward peace between Israel and the Palestinians. Dismantling the Palestinian terrorist infrastructure is the necessary condition. It will be the standard by which Arafat's successors will be measured.

Another one of Israel's neighbors that has demonstrated that it is not capable of dealing with terrorist groups opposed to an accommodation with Israel is Lebanon. The Hizbollah terrorist organizations - financed, equipped, and trained by Iran and backed by Syria - has in effect hijacked southern Lebanon, the area bordering on Israel, and is preventing the normalization of relations between Lebanon and Israel. The Lebanese government, being incapable or unwilling to discipline Hizbollah, continues to be in a state of war with Israel.

The paramount effect of the groups engaged in terrorist activity is supported by an analysis, based on game-theoretic considerations, of the conflict between Israel and the Palestinians. It might be viewed as a two-person non-zero-sum game in which resolution of the conflicting claims would benefit both players, to the extent that both players perceive the penalties involved in the concessions they will be making to be smaller than the penalty incurred by the continuation of the conflict.

This picture differs from reality in a number of ways, but primarily because no single actor represents the Palestinians. Hamas, Islamic Jihad, the PFLP, and the PLO, which itself is not in full control of all the faction associated with it, are active participants (usually spoilers) in the "game." This picture emphasizes again that disciplining these various groups and allowing the Palestinians to speak with a single voice in the negotiations is a necessary condition for useful negotiations to proceed.

In other words, suppressing the terrorist threat from a number of Palestinian groups, which is directed against Israel as well as against the more moderate Palestinians, is the first step for negotiations leading to a resolution of the conflict to proceed. Israel's battle against Palestinian terrorism over the past three years has made a significant contribution to accomplishing this task. Are Arafat's heirs going to finish the job? Progress toward peace in the area hinges first and foremost on the answer to that question.