Libya's agreement to pay compensation to the victims of a bomb attack against a West Berlin nightclub will help to normalise ties between Tripoli and the European Union.
The diplomatic thaw has been under way for some time but it gained critical momentum in December 2003 with the surprise announcement that, after secret negotiations, Britain, the US and Libya had reached a deal under which Muammar Gaddafi's regime would abandon its programmes to build weapons of mass destruction.
International inspectors quickly went to Tripoli.
EU leaders still have some concerns about Gaddafi's Libya
Libya gave a full account of its activities. Its nuclear programme was dismantled and what stocks it had of chemical weapons were rapidly destroyed.
But weapons of mass destruction were not the only issue. The US has long viewed Libya as a country which sponsored terrorism.
Here too, Libya has seemingly turned the page.
Progress has been slow and inevitably there have been bumps on the way.
The deal now agreed in relation to the bombing of a West Berlin night-club joins two other compensation agreements relating to attacks on US and French airliners - the destruction of a Pan Am flight over Lockerbie in 1988 and the bombing of a UTA DC-10 airliner over Niger in September 1989.
Earlier this year, in return for this dramatic shift, the UK Prime Minister Tony Blair visited Tripoli.
And, in a highly theatrical visit involving a tent especially flown in for the occasion, the Libyan leader pitched up, literally, at the EU in Brussels.
April 1999: Libya hands over suspects in bombing of Pan Am flight over Lockerbie
January 2002: The US and Libya reveal they are in talks to improve relations
August 2003: Relatives of Lockerbie victims agree $2.7bn payout from Libya; Tripoli takes responsibility for the bombing
September 2003: UN Security Council votes to lift sanctions
December 2003: Libya announces it will halt programmes to develop weapons of mass destruction
December 2003: UN nuclear inspectors begin checks
January 2004: Relatives of 170 victims of the bombing of a French airliner in 1989 sign a $170m payout deal with Libya
EU economic sanctions against Libya were removed and US-imposed sanctions significantly eased.
The EU and the Americans still have some concerns about Libya.
Both stress human rights issues.
The EU, in particular, is alarmed at the fate of six foreign medical workers - five Bulgarian nurses and a Palestinian doctor - who have been sentenced to death for allegedly infecting hundreds of Libyan children with HIV.
The Bush administration, too, has its reservations about the Libyan regime.
But there is no doubt that Libya is now seen as a country with which the wider international community can do business.
Of course, there is great debate about what prompted the Libyan government's change of heart.
The Bush administration likes to point to the invasion of Iraq as providing Colonel Gaddafi with a salutary warning.
But the Anglo-US negotiations with Libya pre-dated the war.
Some analysts believe that Colonel Gaddafi's essentially secular regime feared a challenge from Islamist unrest unless economic conditions improved.
Pressure on Libya seems to be a classic example of multilateral action working.
It seems that it was Libya's economic isolation and ageing oil infrastructure that finally brought Colonel Gaddafi in from the cold.