Many voters arrived hours before polling stations opened - some wrapped in blankets, clutching mugs of hot drinks.
By midday, most of the main political figures had voted.
Mr Mandela had already pledged his support to the ANC at a rally last week, but Mr Mbeki was widely rumoured to be considering backing Cope.
After casting his vote in Johannesburg, Mr Mbeki did not confirm the speculation, saying: "People should vote for who they want, not out of fear, but for the party they believe will deliver the South Africa they want."
In a polling station queue, the leader of the official opposition Democratic Alliance party, Helen Zille, told the BBC that South Africans needed to "stop Zuma to save the constitution".
"He's a one-man constitution-wrecking machine and what he says and what he does are two different things," she said.
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