David Cameron is the clear favourite to lead the UK Conservative party among Scottish Tory MSPs.
The candidates will embark on a series of hustings
Ten out of the 18 Tory MSPs in the Scottish Parliament told the BBC's Politics Show they wanted David Cameron to win the leadership contest.
Only two said they would prefer David Davis to succeed Michael Howard as the party's UK leader. Three said they had still to make up their minds.
Three others refused to reveal how they would vote in the ballot.
Tory MSPs for Cameron
Lord James Douglas Hamilton
These included the party's Scottish leader David McLetchie and his deputy Annabel Goldie.
Health spokeswoman Nanette Milne also refused to reveal her intentions.
MSPs Alex Johnstone and Brian Monteith endorsed Mr Davis.
David Mundell, the former MSP who is now the Tories' sole Scottish
representative at Westminster, has been campaigning for Mr Cameron.
He said he was encouraged but not surprised by the findings.
Mr Mundell said that Mr Cameron was a "relaxed young man with a clear and positive vision" for both the party and the country.
The outcome will be decided by the votes of party members throughout the UK.
The two rivals will battle over the next six weeks to be named leader when the results are announced on 6 December.
Strong support for Mr Cameron at Holyrood was likely to boost his Scottish campaign.