One of the Middle East's biggest, least-discussed mysteries has been how to understand Israelis. This is a long, complex subject. But so many, including Arab friends, have asked me to explain this issue that there is an obvious need for clarification here. So here we go. From 1967 on, Israelis had a great debate. Both sides, Left and Right, agreed that the Palestinians and most Arab states were not ready for peace. But the Left thought big concessions could bring a permanent political deal once the other side began to change. The Right doubted this would happen, and believed settlements in the captured territories would consolidate control there. Only a small minority saw permanent retention of the territories as a religious obligation. Most Israelis saw holding that land and building settlements in tactical terms. By the end of the 1980s, signs of a real shift in Palestinian positions were still limited. But in the early 1990s Iraq's defeat by a US-led coalition and the PLO's low point seemed to offer a true opportunity. Rather than try to crush the Palestinian movement forever - something that would have fit the demonize-Israel stereotype - the country offered confidence-building measures and concessions in exchange for real peace. The result: the 1993 Oslo agreement and the ensuing peace process. WITH THE long-awaited moment perhaps at hand, debate within Israel shifted. The Left claimed that Palestinian leader Yasser Arafat would make and implement a compromise peace. The Right claimed he would do so, and then break it. Hardly anyone believed Arafat would turn down a good deal. The test came with the Camp David meeting in mid-2000 and the offer by President Bill Clinton, with the agreement of Israeli prime minister Ehud Barak, at the end of 2000. The final offer - and even this was only the starting point for negotiations - was a West Bank-Gaza Strip Palestinian state with the equivalent of all the pre-1967 land (with small swaps to make up for Israeli annexation of a few areas), including a capital in east Jerusalem and massive reparations payments. Arafat turned it down, and instead launched a campaign of renewed violence and terrorism. At this point, Israeli perceptions were turned upside down. The high hopes of the 1990s - even my conservative friends, while balking at turning over east Jerusalem, had accepted large concessions and a Palestinian state in exchange for peace - crashed. INTERNATIONALLY, Israelis had suffered two betrayals. First, there was the Palestinian leadership's use of concessions to strike against Israel directly and undermine its position internationally. After all, Israel's own government had dismantled the negative image of the PLO as a movement whose goals were Israel's destruction and whose means was terrorism. On one memorable occasion, some American Jewish leaders rewrote a speech for Arafat to make it sound more moderate. The other betrayal came from the West, especially Europe. For years, Israel had been told that if it made concessions and took risks for peace, it would have international backing if anything went wrong. Now, subjected to a terrorist assault whose bloodiness was made possible by Israel's own admission of so many returning Palestinians, sponsorship for aid to them, and the turning over of territory to their control, Israel also faced the most hostile Western policies and image, too. Within the country, a new consensus emerged, taking one idea from the Left and one idea from the Right. From the Left, most Israelis accepted the idea of giving up the territories and agreeing to a Palestinian state in exchange for real peace. From the Right, the majority concluded that there was not going to be a Palestinian partner for peace or a negotiated resolution for many years to come. Of course, not everyone came to this conclusion, but most did. On this basis, friends of mine who habitually voted for Meretz on the Left now cast their votes for Ariel Sharon to be prime minister. AFTER A half-century of warfare, in which everyone knows someone or has relatives who have died in war or terrorism, most Israelis are still eager for peace. They are not motivated because they think Israel is weak or afraid, but simply by the strong feeling that peace is preferable to war. Digging in for the long run, they backed withdrawal from southern Lebanon and from the Gaza Strip. They were ready to pull out of much of the West Bank as well. Whether these withdrawals were a good or bad idea is another column; yet they were certainly an attempt to show Israel's desire not to "occupy" another people. At that point it was up to the Palestinians to show what they would do with the opportunity. The election of Hamas and the continuation of terrorism was the result. After all this political talk, it should be added that no country in the world - perhaps in history - has had so many rapid psychological ups, downs, and dramatic changes than Israel. Yet public opinion polls show a remarkably high level of personal satisfaction. The economy has boomed; progress continued. Whatever problems the country has, there is a strong sense of optimism and willingness to examine faults to repair them. Which reminds me of how one day I took a US newspaper, walked down Sheinkin Street in Tel Aviv jammed with people, finally found an empty chair in a caf , and read the front-page article, which explained how Israelis were so fearful of terrorism that nobody went out any more. The writer is director of the Global Research in International Affairs Center at IDC Herzliya.