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The ceremony on the White House lawn in Washington was broadcast live on television. The two leaders sealed the deal with a firm handshake, watched by a smiling President Jimmy Carter.
Both President Anwar al-Sadat of Egypt, and the Israeli Prime Minister, Menachem Begin, described the ceremony as an "historic turning point".
Mr Sadat praised President Carter as "the man who performed the miracle".
"Without exaggeration," he said, "what he did constitutes one of the greatest achievements of our time".
Mr Carter, however, was more cautious, saying the treaty was "a first step on a long and difficult road."
"We must not minimalise the obstacles that lie ahead," he said.
Deep divisions between the two sides remain, and even in their speeches following the ceremony the two presidents revealed how far there is still to go.
Mr Begin spoke emotionally of how the city of Jerusalem could never be divided; while Mr Sadat was unreservedly frank about the question of Palestinian autonomy.
News of the signing ceremony was greeted with angry demonstrations throughout the Arab world. Crowds stormed the Egyptian Embassy in Kuwait, and there was a strike in the West Bank.
The PLO leader, Yasser Arafat, told a rally in West Beirut: "Let them sign what they like. False peace will not last."
He accused President Sadat of betraying the Egyptian people, and said they would eventually eliminate him.
The normally moderate King Hussein of Jordan has now joined President Assad of Syria and President Hassen al Bakr of Iraq in calling a summit conference of opponents of the treaty.
Egypt is thought likely to be expelled from the Arab League as a symbolic gesture of anger at the decision to go it alone in negotiating peace with Israel.
Even in the West, the response to the treaty has been lukewarm. A statement from the nine European Community nations praised the efforts of President Sadat and Prime Minister Begin to make peace.
But, in a comment bound to anger the Israelis, it added that a settlement could only happen if the Palestinian people were given a homeland.
The Egypt-Israel peace treaty was a direct result of the Camp David Peace Accords, signed in September 1978. President Sadat and Prime Minister Begin were jointly awarded the Nobel Peace Prize later that year.
Under the accords, Israel agreed to withdraw troops from the Sinai Peninsula in return for Egypt's recognition of the state of Israel. Palestinians were also granted the right to some self-determination.
President Sadat died for his decision to shake hands with Israel, assassinated in 1981 by extremists in the Egyptian army opposed to the treaty.
The last Israeli troops left the Sinai Peninsula in 1982. Less than two months later Israel invaded Lebanon. There was little further progress towards peace in the Middle East until the Oslo Peace Process began in 1993.
In August 2005, Israel put into force its so-called Disengagement Plan and evicted Jewish settlers from the Gaza strip and began to demolish some settlements on the West Bank as well.
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