Sir Patrick Mayhew, the Secretary of State for Northern Ireland, said after talks between the parties at Stormont, in Belfast, that they had agreed to move to the second strand of the process - direct talks involving the main democratic parties and the two governments.
It also paved the way for the third strand of talks to take place in parallel, between the two governments over the relationship between the North and the Irish Republic.
Although there was a preliminary meeting with Irish ministers on Wednesday, it will be the first time that the Ulster Unionists have been involved in direct negotiations with the Irish government since the ill-fated talks in 1974 on a power-sharing administration at Stormont. For the Democratic Unionist Party, which was held out of those talks, it will be the first negotiations with the Republic since partition 70 years ago.
Sir Ninian Stephen, the former governor-general of Australia, is standing by to act as the independent chairman for the first meeting, which is likely to be in London. If there is no breakdown, it will be followed by further talks in Belfast and Dublin.
Yesterday's talks centred on the first stage of the process, on agreeing a structure for an assembly with devolved powers for Northern Ireland. Although differences remain, the parties agreed to move to the next strand of the talks on devolved power and cross-border relations.
The Ulster Unionists, led by James Molyneaux, the Democratic Unionists, led by Ian Paisley, and the non-sectarian Alliance Party, led by John Alderdice, are pressing for an elected assembly run by committee reflecting party strengths. But that form of power sharing has been rejected in the private talks by the nationalist SDLP, led by John Hume.
Mr Hume is seeking a European-style administration, headed by three commissioners appointed by London, Dublin and Brussels, with three more elected in Northern Ireland.
Sir Patrick has come close to accepting the elected body proposed by the three other parties, in spite of the SDLP's reservations, but yesterday's progress showed he had succeeded in maintaining a delicate balance to keep Mr Hume's party engaged in the talks.
The agenda for the final strand of the talks will include the possible surrender by the Irish government of articles one and two of its constitution laying claim to the six counties of Northern Ireland. But in return, Dublin has insisted that the pooling of sovereignty over Northern Ireland must also be open for discussion.
It remains unclear whether ministers would press ahead with legislation to create some form of power-sharing assembly in Northern Ireland along the lines proposed by the Ulster Unionists, DUP and Alliance parties, if the talks find no over-arching formula for agreement. But Sir Patrick has made it clear he wants to see progress.
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