Mr Molyneaux's departure after 16 years at the helm has presented the party, which represents the bulk of the Protestant population, with a defining moment. Within the next three weeks it faces the choice of voting in a "safe" candidate or opting for a new departure.
Of the four main candidates, who are all MPs, Ken Maginnis favours an accommodation with nationalism, William Ross and the Rev Martin Smyth are traditionalists and John Taylor - the early frontrunner - is viewed as a strong if unpredictable individualist.
The party has stood aside from the peace process which has just delivered almost a year free of shootings and bombings. Its representatives refuse to meet Sinn Fein and have been sceptical observers on the sidelines rather than participants.
Its critics say its leading figures have had problems adjusting to the radically changed political situation.
The choice of leader could have important implications for the Government in that John Major, with his slender Commons majority, will be considering whether the nine Unionist MPs could be induced to support him. Mr Molyneaux was at first supportive of the Government but in the spring his party was outraged by what it regarded as the anti-Unionist tone of the framework documents which Mr Major published with Dublin.
Mr Molyneaux's strategy of relying on his pull in the corridors of power was henceforth considered a failure.
A "stalking-horse" candidate in the leadership election in March secured an unexpectedly high vote, indicating a high level of disappointment in his performance. The loss of the North Down by-election in June was another setback which made it clear the Molyneaux era was drawing to a close.
In anticipation of the coming contest, both Mr Maginnis and Mr Taylor have moved towards the centre of the party, Mr Maginnis taking a harder line while Mr Taylor has made unusually conciliatory comments.
They differ sharply on the peace process: Mr Maginnis has said that the IRA has decided to call off the ceasefire, but Mr Taylor has said he believes it is "for real".
The Sinn Fein President, Gerry Adams, said the peace process represented a decisive moment in history, adding: "Recent opinion polls suggest that Unionist grass roots are ahead of the politicians on the need for flexibility. I am confident that any Unionist leader who is prepared to reach out to his nationalist neighbours would more accurately reflect Unionist hopes for the future."
Last night, Mr Adams and the Irish Prime Minister, John Bruton, repeated calls for all-party talks. A joint statement following a meeting in Dublin said inclusive talks should go ahead, but it made no reference to the continuing row over weapons decommissioning
The Unionist leader announced his resignation in a manner characteristic of his low-profile approach to politics, sending out a short fax which said that on Sunday, on his 75th birthday, he had decided to resign to allow a successor to prepare for the next general election. The fax concluded: "Might I make it absolutely clear that I have no intention of making further comment on my decision." He then disappeared from view.Reuse content