And, as President Clinton will learn in Damascus this week, this does not just mean the return of all the Golan Heights to Syria. Mr Assad wants a real peace throughout the region and particularly in the West Bank and Gaza, because he knows that without it all the Arab regimes will be in danger - whether or not they sign a peace treaty with Israel. How Mr Clinton, the most pro- Israeli US president in a generation, deals with this demand will be a real test of diplomacy. There are those in the region who fear he may not even understand it.
Part of the problem is that, over the past months, the world has been presented with a very misleading picture of events in the Middle East. The official Washington-Tel Aviv version of events is as follows. Peace is breaking out in the region. The PLO has signed up for peace, Jordan is about to sign and only Syria is holding out - perhaps until the end of the year.
Opponents of peace - mindless, faceless and evil - are trying ever harder to destroy the lives of future generations of Arabs and Jews by a campaign of 'terrorism' - or 'pure terrorism', to use the odd phrase of Uri Dromi, the Israeli government's official spokesman.
This is how the 'peace process' has been represented on television, in editorials, by almost all Western governments. Just get the rest of the Arabs to sign up, crush the 'terrorists' and the story is over.
History, however, is not like that. The Arabs are not signing up because they suddenly desire peace. They are doing so because the Cold War is over and the superpower that supported their struggle - unlike Israel's supporter -has disappeared. As winner of the Cold War, the US is dictating the peace and many millions of Arabs - Arab people, not Arab governments - regard this peace as deeply humiliating.
Yasser Arafat's 'declaration of principles' - how disturbing that last word seems today - has given him the garbage pit of Gaza and the village of Jericho and near civil war with his own people. He is no nearer to controlling the West Bank. The Jewish settlers are not leaving his land.
Occupied territory, as it is designated under international law, must now be called 'disputed territory', according to the State Department's rubric - as if Israel might be the owner - while the Palestinian diaspora (more than half the Palestinian population) have lost their 'right to return'.
Squeezed between the isolation of Iraq, the suspicion of Syria and the occupied West Bank, King Hussein - facing an ever graver economic crisis - signs up this week. His relationship with Israel is unique, but Jordan's pledges over four decades - never to make peace while east Jerusalem and the West Bank remain occupied - have been abandoned (because Mr Arafat has been forced into a separate deal). Unable to persuade the Israelis to leave all Jordanian territory, the king has to 'lease' his own land to the Israelis to resolve the peace.
Syria is now ever more isolated, still on the American list of states that sponsor terrorism but finding its own bargaining platform eaten away by the desertion of Arab allies and the extinction of the Soviet Union. Even if the Israelis do leave all of Golan, Syria is likely to find US peace-keeping troops on its land - as a UN force, of course - while Syria's self-declared status as vanguard of the Palestinian struggle will look ever more implausible if Israel remains in east Jerusalam and the West Bank.
Yet still we ignore these strains within the Arab world, accepting the double standards that have plagued the Middle East for so many years. Our justified horror at the vicious bus bomb in Tel Aviv was not repeated when Israeli tank shells tore seven civilians to pieces in southern Lebanon the very same day; indeed, the event was scarcely reported. It was as if Israeli lives mattered more than Arab lives, a conclusion voiced by the Lebanese relatives of the dead last week. The world reported the Hamas bomb as an act of 'terrorism', a word it was not prepared to use when the Israeli settler Baruch Goldstein murdered even more civilians in the Hebron mosque last February. The house of the Hamas bomber's family was to be demolished as a collective punishment. Yet after the Hebron massacre, Goldstein's home was protected by Israeli troops lest angry Palestinians attack it.
Mr Arafat, meanwhile, is being urged to destroy Hamas, to perform the same task for Israel as its puppet, Lebanese General Antoine Lahd, is supposed to do in the south of Lebanon: to protect Israel from 'terrorists'. Each day, Mr Arafat's power and prestige - such as it was - is further diminished. A few weeks ago, he hoped to disarm Hamas, not militarily but by fighting his fundamentalist opponents in self-rule elections. Then just last week, a PLO spokesman at the Palestinian-Israeli talks in Cairo revealed that the PLO had agreed to an Israeli demand to exclude 'hardliners opposed to peace' from the poll. Not only are the elections to be rigged on behalf of the PLO, therefore, but any idea that Hamas can be brought into politics has been thrown away. Now it will have to be fought.
And it will probably fight back. Although they ostensibly demand an Islamic republic in all 'Palestine' - and thus the destruction of Israel - the leadership of Hamas cannot believe that murdering Israelis will bring this about. The aim of their bombing campaign is surely to turn Mr Arafat into Israel's creature and thus destroy him. By forcing Mr Arafat to go to war with Hamas, which is apparently what the Israelis also want, Hamas will prove that he no longer represents the Palestinian people.
And with the destruction of the secular Arafat, Palestinians will be urged to turn to Islam in a renewed struggle against Israel. The irony is that if Mr Arafat does go to war with Hamas - and Gaza burns - this will also provide final 'proof' to the Israelis that the PLO leader has 'failed the test of statehood'; presiding over such anarchy, the Israelis will say, he cannot be entrusted with yet more territory.
By this time, all the Arab states will have signed up for peace. There will be no Jordan or Syria or Lebanon - certainly no Egypt - to offer the Palestinians help. There will be no stopping further Jewish settlements then. Indeed, the Arab states are already powerless to stop Yitzhak Rabin building more Jewish housing east of Jerusalem, as he is doing this very month. But Israelis as well as Arabs remember history.
And it is a fact that the Palestinian tragedy has been the cause, directly or indirectly, of every Middle East war, the enduring reason for all Arab- Israeli enmity, the origin of the death of every Egyptian, Israeli, Jordanian, Lebanese and Syrian soldier. Without a just and fair settlement - which the PLO-Israeli agreement seems further than ever from providing - there will be no ultimate peace.
However many states may sign treaties with Israel, they will find their people increasingly humiliated and restive, demanding with growing anger the wars against Israel that the 'peace process' was supposed to eliminate forever. Both Arabs and Israelis deserve peace - which is why Mr Assad will want to talk to Mr Clinton about peace 'with honour'.