The Ulster Unionist leader and a hardline MP have said they are confident of support from their constituency associations, despite facing votes of no confidence.
Both MPs are facing votes of no confidence
David Trimble is facing a vote of no confidence in him as Member of Parliament for Upper Bann, whilst anti-Agreement MP Jeffrey Donaldson is facing a similar vote in the Lagan Valley constituency.
It follows the latest wrangle between the two MPs which is due to take centre stage at a meeting of the party's ruling council next Monday.
Party members in the Upper Bann Ulster Unionist constituency are seeking an extra-ordinary meeting of the party's local association to vote on the no confidence matter.
On Friday morning, a petition will be handed into the constituency secretary.
Sceptics within Mr Trimble's association say they have 25 signatures, which they claim is enough under party rules to require the meeting to be held.
They say they believe the meeting will be held within the next two weeks.
Earlier this week, Mr Trimble met his constituency colleagues to discuss ongoing concerns about party policy.
His failure to reassure some members has left him facing the vote.
Robert Oliver, who is behind the petition, said Mr Trimble had done good work as an MP, but had not listened to a "large percentage of the people who put him where he is today".
Meanwhile, members of the Ulster Unionist Association in Lagan Valley have presented a 70-strong petition seeking a vote of no confidence in their MP, Jeffrey Donaldson.
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Ivan Davies, who is one of 10 councillors who have signed the petition, said some people were "increasingly concerned that Jeffrey has not been accepting the democratic decisions of the Ulster Unionist council".
However, Mr Donaldson said he had no doubt he would be supported by his constituency association.
The Ulster Unionist leader will try to face down his critics next Monday at a meeting of the party's ruling council.
It will look at a motion rejecting proposals which are linked to the British-Irish joint declaration.
The meeting has been convened at the request of sceptical party members led by Mr Donaldson.
Last month's joint declaration outlined plans to reduce troop numbers to 5,000 as part of an attempt to move the political process forward in Northern Ireland.
On Tuesday, defence secretary Geoff Hoon said there were no plans to disband the home service battalions of the RIR.
Mr Hoon was responding to speculation that the Army planned to disband the units once demilitarisation proposals in the recent British-Irish joint declaration were fully implemented.
Mr Trimble said the news was a "welcome development" but Mr Donaldson said it required more clarity.
The joint declaration included five annexes dealing with security normalisation, policing and justice, human rights and equality, on-the-run paramilitaries and mechanisms to verify and monitor any deal.
Last month, two Army watchtowers were taken down near the border in south Armagh as part of the joint declaration.
Northern Ireland's devolved administration was suspended last October amid allegations of IRA intelligence gathering in the Stormont government.
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