Mr Trimble, the Ulster Unionist leader, described the occasion as workmanlike while Mr Adams, the Sinn Fein president, said there was no acrimony. The low-key presentation by the two men made the potentially historic encounter seem positively mundane.
The two political opponents have been in the same room on numerous occasions during the negotiations of the past year, but yesterday was the first time they have addressed each other directly.
They were among the leaders of parties of the new assembly who convened at Stormont to discuss various administrative matters. A further step will be taken on Thursday when the two men will have their first bilateral encounter.
Stormont still bore traces yesterday of last week's Clinton visit which was instrumental in bringing about the new forms of contact. Four pieces of sticky tape were still on the ground outside the front door: they had been placed there to show Bill Clinton, Tony Blair, David Trimble and his deputy Seamus Mallon where to stand to wave for the cameras.
During yesterday's meeting Mr Trimble, who chaired the proceedings, looked at the Sinn Fein leader and said "Gerry Adams", inviting him to speak. According to Mr Trimble later: "The only point of contention was when Sinn Fein representatives raised the question of the formation of the shadow executive.
"We pointed out that, under the agreement, a number of things must happen, that there must be progress on a number of things, that there must be progress on all matters, and this puts a particular responsibility on paramilitary-related parties."
Mr Adams said the encounter had been "good engagement", adding: "I think the meeting was conducted in a good atmosphere and there was no acrimony." He said no pre-conditions lay in the way of Sinn Fein's participation in the new executive, insisting that parties had an automatic right of involvement.
Yesterday's meeting produced no conclusions on issues such as how many departments there should be for the new Northern Ireland administration, although there is a broad consensus that there will probably be 12. There was also no decision on when the shadow executive should come into existence.
In the meantime, however, the major parties have ensconced themselves in the large building which housed the Stormont parliament until its abolition in 1972. The building has since played host to a number of other assemblies, all of which ended in failure.
The parties are using the buildings offices and facilities such as the assembly members' dining room. Ad hoc committees are already functioning in advance of next Monday, when the assembly will reconvene following the summer break.
t The funeral took place yesterday of the 29th victim of the Omagh bombing, who died at the weekend. The service for Sean McGrath, 61, who was married with four grown-up children, was held in Killyclogher, Co Tyrone.Reuse content