Britain's interior minister Theresa May and justice minister Michael Gove are the frontrunners to replace Prime Minister David Cameron, who announced his resignation in the wake of the historic vote to leave the EU.
Both candidates have promised to lead Britain out of the European Union following last week's referendum but have said they do not plan to start formal negotiations immediately, as demanded by EU leaders.
Cameron, who had campaigned to stay in the EU, has said it will be up to his successor to invoke Article 50 -- the formal procedure for leaving the bloc.
Article 50 sets a maximum two years for negotiations, after which Britain would automatically be out of the EU unless member states agree unanimously to extend the deadline.
Cameron's successor as Conservative Party leader and therefore also prime minister will be unveiled on September 9 ahead of a party conference in October.
Based on what May and Gove have said in launching their leadership bids this week, here are the two candidates' stances on some key policy issues:
May, who backed the "Remain" camp in the referendum, has said Article 50 "should not be invoked before the end of the year", adding: "There should be no decision to invoke Article 50 before the British negotiating strategy is agreed and clear."
Gove, one of the leaders of the Brexit campaign, made similar comments, saying: "I have no expectation that it will be triggered in this calendar year".
"We need to have some preliminary conversations before doing so... We will do it when we're good and ready," he said.
May said she wanted "action on free movement" and to "regain control of the numbers of people who are coming here from Europe" without giving details.
She said it was not possible to cut immigration, one of her current ministerial responsibilities, by "pulling a lever".
Gove said: "I will end free movement, introduce an Australian-style points-based system for immigration, and bring numbers down."
But he admitted that immigration numbers could not be reduced to tens of thousands "until we're outside the European Union".
Some 270,000 EU migrants came to Britain last year.
May said she would negotiate the "best possible access for trade in goods and services".
"It must be a priority to allow British companies to trade with the single market in goods and services," she added.
Gove says Britain would leave the single market and negotiate a series of bilateral trade deals with other countries.
Britain's new leader does not have to call a general election to be confirmed in office and both Gove and May have ruled one out before the next scheduled poll in 2020.
May has also excluded a second referendum on the terms of Britain's exit from the EU -- a possibility mooted by some "Remain" supporters.
The two candidates have also both gone out of their way to stress their sober, even boring, images to a public facing uncertainty and turbulence.
As he addressed reporters in a suit and tie, the bespectacled Gove said: "Whatever charisma may be, I don't have it. Whatever glamour may be, I don't think anyone could associate me with it".
May, who wore a sober tartan trouser suit, said: "I know I'm not a showy politician.
"I don't tour the television studios. I don't gossip about people over lunch. I don't go drinking in Parliament's bars. I don't often wear my heart on my sleeve. I just get on with the job in front of me."