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Mr. Mubarak has also enforced the “cold peace” that Sadat signed with Israel in 1979, and he proved a valuable American ally in the peace process of the 1990s.

His General Intelligence Service, led by Omar Suleiman, played a key role in training the preventive security services for the Palestinian Authority during and after the Oslo peace process. At regional Arab League summits, Mr. Mubarak was almost always a voice and a vote against the more anti-American currents in Middle Eastern politics.

In 2007, Mr. Mubarak pushed a new law through Egypt’s People’s Assembly that would make the speaker of the assembly president for 60 days while he oversaw arrangements for a special election. The new law requires anyone standing for that election to be in the leadership of a political party for at least one year.

While Mr. Mubarak has declined to endorse a successor, the new law on presidential succession provides a major advantage to Mr. Mubarak’s son, Gamal Mubarak, 47. The younger Mr. Mubarak is head of the powerful policy committee of the ruling National Democratic Party (NDP), the party that has led Egypt’s government for more than 50 years.

Other potential military rivals to Gamal Mubarak, whose nickname is “Jimmy” in U.S. policymaking circles and among the Egyptian elite such as Mr. Suleiman, are not formal members of the NDP.

Mohamed ElBaradei, the former chief of the International Atomic Energy Agency, who is campaigning to end the emergency law and open the Egyptian political system to more competition, would also not qualify to run for president if Mr. Mubarak dies in the next year.

“There is a very serious and precise process for presidential elections and presidential succession if the sitting president becomes incapacitated,” said a senior Egyptian government official. “That process is competitive, and the notion that it is somehow predetermined is completely false.”

Despite the new rules, Egypt has faced political ferment in recent months to open up the political process through the emergence of Mr. ElBaradei, who provides Egypt’s opposition with a figure who has international recognition. Mr. ElBaradei won the Nobel Peace Prize in 2005.

Mubarak has been president of Egypt for 30 years, and this will be an historic event when it occurs,” a senior State Department official said of Mr. Mubarak’s anticipated demise. “You have Gamal Mubarak as a prospective replacement, but you also have ElBaradei as someone who is prepared to compete for the presidency under specific circumstances.”

The official said the Egyptian government will face a historic decision after Mr. Mubarak dies, and ultimately it will have to account for the wishes of the Egyptian people for more openness after years of authoritarian rule.

“In some ways, the presidential campaign has already started,” the official said. “This is different than the dynamic you see in other countries. There is some open space in Egyptian society, but there is not yet enough to enable a genuinely competitive election among candidates, where more than one have a true opportunity to win.”

Frank Wisner, a U.S. ambassador to Egypt between 1986 and 1991, said he had faith in the process of transition already established by the 2007 amendments to the constitution.

“I don’t know who is going to succeed the president. I have no idea the exact formula that will be followed,” Mr. Wisner said. “I assume the successor to the president of Egypt is someone we know. I don’t know what his name is, but I know he will seek Egyptian stability and seek the friendship with the United States that has dominated Egypt’s approach in the Mubarak era.”

In recent months, some bipartisan former government officials and analysts who call themselves the Working Group on Egypt started meeting with senior officials in the Obama administration to make the case for a U.S. policy of encouraging democratic reforms.

Brian Katulis, a scholar at the Center for American Progress and a member of the working group, said: “We all know some sort of change is happening in Egypt, whether it is Mubarak’s departure from the scene, or more ferment on the Internet. There is an opportunity from a U.S. policy perspective.”

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