A number of those who took part in the meetings, which involved both the Ulster Volunteer Force and Ulster Defence Association, said there had been lengthy discussions on a ceasefire, adding that this now seemed closer.
Pressure has been mounting on the loyalist groups to end their violence since the IRA announced a cessation of its military campaign at the end of August. Although their attacks have not ended, they are at a low level and have caused no fatalities for some weeks.
On Monday, about a dozen senior loyalist figures were allowed into the Maze prison near Belfast, which houses most of the loyalist and republican hardliners. Half of them met UVF prisoners while the rest spoke to UDA inmates.
Both organisations maintain command structures within the prison, headed by 'O/Cs' (officers commanding). These are believed to have taken part in Monday's meeting, together with two members of the UDA's inner council in custody awaiting trial.
Optimistic assessments of the meetings came from those associated with both groups yesterday. David Ervine of the Progressive Unionist Party, which has links with the UVF, said he believed the possibility of a ceasefire was now closer.
He said Northern Ireland had been 'a very jittery place' when the IRA announced its ceasefire, but since then confidence had grown and was still growing. The prison meetings were extremely important, he said, because input from the prisoners was vital.
He added: 'The debate is intense and one hopes it will reach a positive conclusion.'
John White, who is prison spokesman for the UDA-linked Ulster Democratic Party, said an obstacle had been removed because no agreement could be reached unless dialogue was opened up with the prisoners. A possible ceasefire had been discussed in great depth.
Mr White, a former life prisoner, said the inmates had made it clear that any settlement could not include concessions which would erode the constitutional position of Northern Ireland within the United Kingdom. He added: 'Their main concern was to bring about peace and stability in order that their children, and future generations, will not have to come through what they had to come through this last 25 years.'
The Northern Ireland political affairs minister, Michael Ancram, said the Secretary of State for Northern Ireland, Sir Patrick Mayhew, had allowed the meetings to take place because he did not want to impede a dialogue which might lead to a cessation of loyalist violence.
The pace of events now appears to be accelerating in the loyalist paramilitary underworld. Sources who earlier this week were indicating that a ceasefire decision was unlikely before the end of October were yesterday saying that it could come more quickly.
Like the IRA, however, there are no signs that the UVF or UDA are contemplating their own disbandment. Although the loyalists will be keen to be involved in future negotiations, they do not have the same political ambition as republican leaders, and may well, in terms used by such groups in the past, 'reserve the right to take defensive or retaliatory action'.
Powell's Ulster call, page 7