Britain is adamant: The Irish Republican Army (IRA) and Sinn Fein are two parts of the same organization.
Sinn Fein leader Gerry Adams asserts they are separate and distinct.
Upon this bitterly contentious issue, peace in Northern Ireland now appears to hang.
On Monday in Dublin, Britain's Northern Ireland Secretary Mo Mowlam told Mr. Adams that Belfast police had clear evidence of IRA involvement in two murders last week. This, she said, broke the "Mitchell rules" on nonviolence and meant that Sinn Fein, which had signed the rules, must be excluded from the peace talks.
Her statement triggered immediate complaints from leaders of Sinn Fein that it is an independent party that does not speak for the IRA and cannot be accused of its crimes.
Adams instructed his lawyers to seek an injunction in Irish courts against the ruling. Dublin, with signs of apparent reluctance, sided with the British and ordered its lawyers to contest Sinn Fein's claim that it was being denied "natural justice," the right to be given details of the accusation.
For Adams, expulsion from the talks would be a serious blow. Almost certainly it would mean having to cancel a planned visit to the United States later this month, because US officials would be bound to line up with London and Dublin and decline to meet with him.
On Monday, Adams said the group would battle "tooth and nail" to stay in the talks, claiming Sinn Fein had an electoral mandate from Northern Ireland voters. Sinn Fein said it was planning a series of street protests throughout Northern Ireland.
More ominously, Martin McGuinness, Sinn Fein's chief negotiator, warned that if the British government's view prevailed, "events on the ground" (presumably an upsurge of IRA terrorism) "might make Sinn Fein's return to the peace talks impossible."
Earlier, David Trimble, leader of the Ulster Unionists, Northern Ireland's largest political party, had demanded Sinn Fein's expulsion. He claimed that it and the IRA were "two sides of the same coin," and that the peace process "should continue without Adams and his colleagues."
Adams has battled for years to maintain the claim that Sinn Fein is a stand-alone body, separate from the IRA, and that he himself has never been involved in terrorist acts. He has done so in the face of apparently persuasive evidence to the contrary.
Sean O'Callaghan, a former IRA commander in Ireland, claims that Adams is "the single most important individual within the republican movement for over 20 years" who began as "a young Belfast militant."
No one, however, has produced conclusive proof that Adams once belonged to the IRA, or substantiated Ulster Unionist claims that he is still a member of its ruling council. Attempts to prove that Mr. McGuinness was an IRA field commander in the 1970s have also failed.
In a typical reaction to such claims, McGuinness in mid-1996 told a British government minister: "I am not a member of the IRA, and Sinn Fein is not the IRA's public face." Like Adams, he has stuck to that line ever since.
British and Irish officials concede privately that there are risks in isolating Sinn Fein, and that without its presence at the negotiating table the peace process would have little meaning.
That is why Ms. Mowlam has indicated that the party's exclusion may only be temporary. Currently, the Ulster Democratic Party is suspended from talks because of its links to loyalist terrorist groups. But even limited "punishment" would hurt the timetable for reaching a political solution by late May.
A potential weak point in Britain's insistence that Sinn Fein must pay the price of the alleged IRA killings is that Mowlam has failed to offer any proof. This, she has explained, is because three men have been charged with one of the murders, and so no details may be disclosed.
As Sinn Fein struggled to stay in the talks, there were signs yesterday that the Irish government was embarrassed by having backed the British view.
Usually Dublin and the nationalist Social Democratic and Labour Party agree on their approach to the peace process. But SDLP leader John Hume has signaled that he is against Sinn Fein's exclusion, unless proof is produced that the murders were intended to influence talks, and that Sinn Fein was responsible for the IRA's alleged actions.
Irish Prime Minister Bertie Ahern has said only that Dublin police believe Sinn Fein has "a case to answer."