British Prime Minister Mr Tony Blair welcomed the Northern Ireland Assembly election of Mr Trimble and Mr Durkan and praised the Alliance and the Women's Coalition for their part in the process.
He said: "I would like to congratulate David Trimble and Mark Durkan on their election today as First and Deputy First Ministers in Northern Ireland.
"Their election means that all the institutions foreseen in the Good Friday Agreement are now up and running. That is a major achievement.
"It shows that politics can and does work even where fundamental political differences remain.
"The people of Northern Ireland today can look forward to a sustained period of stable government - local politicians addressing their local concerns.
"They can do so because political leaders have shown the courage and perseverance to keep at the task of implementing the agreement despite all the difficulties," Mr Blair said.
"And in particular today I would like to recognise the brave and difficult decisions taken by the Alliance Party and the Women's Coalition in recent days, as well as the leadership shown by the Secretary of State John Reid.
"No one pretends that overnight Northern Ireland has left the legacy of the past behind forever. What we do know, however, is that today there is both hope and a realistic chance for a stable and prosperous future," Mr Blair said. PA