Whoever wins is likely to succeed Mr Zuma as South African president.
But their bitter leadership battle has raised fears that the ANC could split before national elections in 2019.
President Zuma can remain head of state until those elections. He has been in office since 2009 and South Africa limits the presidency to two five-year terms.
As delegates gathered for the four-day conference in Johannesburg, Mr Zuma, who faces multiple corruption allegations, has urged the party to unite behind the eventual winner.
The leadership contest is expected to be a close one, with legal challenges a possibility.
President Zuma's office has announced that students from around 90% of South African households will get access to free university education.
There have been a number of protests over the issue over the past few years, with the #FeesMustFall movement demanding free university education for all.
Some might question the timing of Mr Zuma's announcement, at the start of a conference where so much is at stake both for him and the party.
Analysts have also been discussing what might happen to Jacob Zuma after this conference, and whether the ANC will force him to stand down as President of the country.
Local media are reporting that he says he will only agree to a decision by the party to recall him as head of state "if the move did not risk further dividing the ANC".
President Zuma is backing his 68-year-old former wife, Ms Dlamini-Zuma, a veteran politician in her own right who has been critical of the enduring power of white-owned businesses.
Mr Ramaphosa, 65, has spoken out strongly against state corruption and has the backing of the business community.
Recent news that he had a modest lead in the polls was quickly reflected by a rise in the financial markets.
President Zuma, 75, has been the focus of much controversy and he has survived several votes of no confidence in parliament.
He faces numerous corruption allegations but denies any wrongdoing.
More than 5,000 delegates are taking part in the four-day ANC elective conference at the Expo Centre in Johannesburg.
The first major engagement for the new leader will be the ANC anniversary celebrations on 8 January.
The ANC has governed South Africa since the first democratic election more than 20 years ago.
The BBC's Andrew Harding says a question remains whether the ANC is in terminal decline, and what that might mean for South Africa's stability and its future.
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