Mr Clarke has not ruled out standing for leader himself
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Gordon Brown may have to defeat as many as three serious candidates for the Labour leadership, according to former Home Secretary Charles Clarke.
The period after Tony Blair steps down would "turn expectations upside down", he wrote in the Mail on Sunday.
Harold Wilson and Margaret Thatcher were among those who had upset the odds to become party leaders, he said.
Former minister Michael Meacher and MP John McDonnell have already announced they will stand in any contest.
But it is uncertain whether either would gain the support necessary for them to enter a final vote.
Each candidate needs to have the backing of 45 MPs to be considered.
'Puffs of smoke'
Mr Clarke wrote in the paper: "A week is famously a long time in politics.
"But, as in the past, the week between Tony Blair's resignation and the close of nominations for the leadership will be the longest of all."
The former cabinet minister, who has previously criticised Mr Brown as a control freak, has not ruled himself out of a future leadership contest.
"Despite the punditry and puffs of white and black smoke, the outlook at the end of that week when nominations close will be very different from initial expectations," he wrote.
Mr Clarke, who is a staunch ally of Tony Blair, added: "There is enough support for two, three or even four candidates."
Environment Secretary David Miliband is among those being encouraged to mount a challenge, and current Home Secretary John Reid is reportedly considering running.
Mr Blair is expected to step down soon after the local elections on 3 May.