Kenneth Clarke, the 65-year-old former Chancellor and David Cameron, the 38-year-old shadow Education Secretary, will make separate 15-minute speeches to Tory representatives in which each will try to show he is the man to lead the party back to power.
Mr Clarke will deliberately rise above the Conservative Party's internal debates by launching a withering attack on Tony Blair and Gordon Brown, the man most likely to succeed him as Prime Minister. His aim will be to convince the Tories that he would turn them into an effective opposition that would regularly land punches on the Government.
Mr Cameron, meanwhile, will attempt to put himself at the head of the Conservative's modernising wing as he tells the conference that the party is doomed without "fundamental change". He will argue that it will win only if it is in tune with voters' priorities, as it was during the 1980s under Margaret Thatcher.
He will say the party has to make voters and supporters feel good about being Conservatives again and demonstrate it has a "message that is relevant to people's lives today, that shows we're comfortable with modern Britain and that we believe our best days lie ahead".
Writing in The Independent today, Mr Cameron says that: "The Conservative Party has to change more than its policies and presentation. We have to change our culture and attitudes: we have to look, feel, think and behave like a completely new organisation."
The response from the Tory faithful to the two speeches could have an important bearing on the leadership contest. With Mr Davis, the shadow Home Secretary, the clear front-runner, Mr Clarke and Mr Cameron are battling to be the second name on the shortlist of two to be chosen by Tory MPs. The final decision will then rest with the party's 300,000 members.
The Tory high command, which admits this week's gathering will be seen as a "beauty contest", is trying to prevent the conference projecting an image of a divided party that is "contemplating its own navel".
The five runners have bowed to pressure from Conservative Central Office by agreeing not to share a platform with any rival candidate at fringe meetings. Central Office is also trying to use the conference to drive home a message to the public that the party knows it must change.
Francis Maude, the Tory chairman, told the conference bluntly yesterday that two-thirds of voters saw the party as out of touch. He said it had to do "much more" than elect a new leader to have a chance of winning the next election.
"Our party has in past times known great, great days, but we have no God-given right to survive, let alone to succeed," he said.
He said polling discovered half of voters thought the Tories only cared about the well-off, more than half believed they were stuck in the past, 64 per cent viewed them as opportunistic and 67 per cent thought they were out of touch.
Mr Maude told the conference of a former Tory voter he met during the election in Crawley, West Sussex, who said she could not back the party because it wanted to help the rich and disapproved of her as a single mother. "She thought we weren't a party for people like her. It wasn't our leader, it wasn't our candidate, it wasn't our policies. It was the values she saw in our party," he said.
Another ardent moderniser, Theresa May, the shadow Culture Secretary, argued that the Tory party had to demonstrate it was comfortable with modern Britain, a party representative of men and women of every age, race and religion.
She said: "For the small minority who don't accept women, or black or gay people, as their equals, I've got a message: Don't think you'll find a refuge from the modern world here. There is no place for you in our Conservative Party."
Alan Duncan, the shadow Transport Secretary, attacked Tory town halls that tried to prevent civil partnership ceremonies for gay couples from taking place on council premises. "Carry on like that and this party will look like nothing more than a repository for prejudice and spite," he said. "We would all love a world in which people fly the flag, don't abort and don't divorce. But sounding like a mixture of Victor Meldrew and Colonel Blimp does not constitute a coherent policy or a basis for political appeal."Reuse content