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Even as the delegation stepped off the aircraft, to be greeted by beaming Libyan officials, the next phase of Colonel Muammar Gaddafi's extraordinary rehabilitation was being put into place. The former pariah state will welcome a team of three Foreign Office ministers in the coming weeks and will host Tony Blair before the summer.
Over the weekend the Libyan leadership, including Saif el-Islam, Colonel Gaddafi's son, and Shukri Ghanem, the Prime Minister, credited Mr Blair with doing most to bring Libya out of isolation.
"If I had to say who is Libya's closest ally today, I would say Tony Blair and Britain," Mr al-Saif said.
Diplomatic sources said that the turning point could be traced to September 2002, when Mr Blair wrote to the Libyan leader asking him to drop support for the Mugabe regime in Zimbabwe and to dispose of his weapons of mass destruction. "Tony Blair played a very important role. The leader (Gaddafi) trusts him," said Mr el-Islam, who is working on a PhD at the London School of Economics.
"If Tony Blair says that turkeys can fly, then we believe him."
As he spoke, a team of British and American weapons experts and intelligence officers were finalising plans to dismantle Libya's weapons programmes. Equipment designed to make a nuclear bomb is likely to be flown to America in the coming weeks, while stockpiles of chemicals will be destroyed locally.
"It was guns or butter," said Mr Ghanem, who is credited with masterminding Tripoli's volte face. "Developing weapons of mass destruction is long and expensive. We would rather spend the resources on our people."
While Washington insists that Libya has still to prove that it is serious about wanting to rehabilitate itself before its name is taken off the State Departments terrorist list, Western diplomats predicted that normal relations were a certainty. The eight congressmen who descended on Tripoli at the weekend seemed to be in little doubt that the two countries are about to embark on a most unusual friendship.
The US Navy last entered Libyan airspace in the 1980s, when bombers attacked the country on the orders of President Reagan, who branded the Libyan dictator the "mad dog of the Middle East".
This time the Libyan leader was showered with praise. "We are here to reinforce the positive steps taken by the leader of Libya," Curt Weldon, a Republican congressmen from Pennsylvania, said.
In spite of the talk of friendship, both sides want very concrete results from the passionate new relationship.
The next moves will happen in Britain. Mohammad Abdelrahman Shalgam, the Libyan Foreign Minister, arrives in London on Wednesday on the first visit of its kind in decades. He is likely to finalise plans for a return visit by the Prime Minister to Tripoli.
Britain is expected to offer a package of incentives, from helping to retrain and re-equip the Libyan Armed Forces to easing restrictions for Libyan students in Britain and launching a "Know How Fund", modelled on a similar project launched in Russia after the fall of communism.
The Libyans are also desperate to attract foreign investment, in particular from American oil companies.
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