Sir George Gardiner, the Tory MP for Reigate, is being challenged by Sir Anthony Durant, a former Government whip, for the leadership of the Thatcherite 92 Group.
Sir George was the leader of a delegation of the 92 Group executive which was recently shown the door by Mr Major after reports that they were planning to warn the Prime Minister that he should assert his leadership.
Sir George's critics believe that snub by Mr Major damaged his chances of holding on to his chairmanship. If he remains, they expect him to stand down next year, and to be replaced by another Thatcherite, John Townend, chairman of the backbench finance committee.
Sir George was voted off the executive of the 1922 Committee last autumn by Tory MPs seeking revenge against the Thatcherites for trouble over the Maastricht Bill.
Apart from that setback, Sir George has proved a survivor and is odds-on to win the postal ballot for the chairmanship of the 92 Group.
Behind the struggle lies an attempt to draw the sting of the Thatcherites in the party, who have proved troublesome for Mr Major.
Those supporting Sir Anthony believe Sir George has wielded too much power by operating a 'slate' of right-wing candidates in the annual elections for Tory backbench committees.
By co-ordinating its voting power, the 92 Group has taken control of the main backbench committees. The leadership of the party was determined to break that hold.
Sir Anthony denies being a leadership candidate, but right wingers who are supporting Sir George believe it would be seen as a coup by the Major camp.
The Thatcherites are becoming increasingly disillusioned with the 92 Group. There are rumblings about the group has become too big to act as an ideological club, capable of influencing policy.
One option is to create a new caucus from the 92 Group. The result should be announced today.