MPs vote on their preferred choice and the first and second placed candidates continue in the contest. Everyone else drops out. Because it might stop an otherwise popular candidate from winning the top job. Both Ann Widdecombe and Ken Clarke may find it hard to find enough MP-backers to reach the final contest. Ballot papers are sent to every member of the Conservative party - around 250,000 people.
Members can choose between the two candidates and the one with the most votes becomes leader.
The outcome will be hard to predict. No one knows quite how many Conservative members there are or which candidate they are most likely to back. It's widely assumed that members would choose a rightwinger, such as Ann Widdecombe - but last time they were surveyed, before the 1997 contest, most members came out in favour of Ken Clarke, the most leftwing candidate.