The next formal step is production of a new working paper by the talks chairman, former US senator George Mitchell. The British and Irish governments want this to trigger a final burst of negotiation over the next four days. In spite of the optimism, many important points have still to be resolved, most observers believing the talks will "go to the wire" before any final agreement is reached. But many major players are predicting that none of the remaining gaps is unbridgable.
Ulster Unionist party leader David Trimble joined calls for Tony Blair to join the parties at Stormont as soon as possible: "Having people talking in Belfast and in London 400 miles away is not conducive to progress ... there is sense now in bringing people together."
Mr Trimble said he believed major disagreements on key issues could be resolved by Thursday. "If we work out the practicalities of it I think it will not be that difficult." This represents a major shift since last week, when his deputy, John Taylor MP, put chances of success at no more than 5 per cent. Mr Trimble added: "I think the difficulty here can be overcome if people are sensible in their approach to them. Unfortunately, we have had a lot of posturing, with people setting out impossible positions."
The Sinn Fein chairman, Mitchel McLaughlin, told the Frost programme that "an agreement is possible." The Alliance Party leader, Lord Alderdice, said: "We are going to get there. It's looking good. The truth is that not only the outline of a settlement but much of the detail is already filled in."
The Northern Ireland Secretary, Mo Mowlam, said: "What I am sure about is that there will be a relevant piece of paper on Thursday for the simple reason that the party leaders have shown the determination and courage to get there."
Yesterday in Dublin the Prime Minister, Bertie Ahern, held meetings with SDLP leader John Hume, Sinn Fein president Gerry Adams and Ulster Democratic Party leader Gary McMichael.Reuse content