Argentines are going to the polls to choose their next president in a general election that ends 12 years of rule under the Kirchners.
President Cristina Fernandez de Kirchner has served two consecutive terms and, under Argentina's constitution, cannot run again.
Her hand-picked successor, left-winger Daniel Scioli, is leading polls.
But he is expected to face stiff competition from Mauricio Macri, the centre-right mayor of Buenos Aires.
Another candidate, Sergio Massa, a former Kirchner ally, is polling behind Mr Macri, while there are three other names on the ballot paper.
Sunday sees the first round of voting. To win outright a candidate needs 45% of the vote or a minimum of 40% as well as a 10-point lead over the nearest rival.
Otherwise, there will be a run-off on 22 November.
Whoever wins the presidency faces significant economic challenges.
While the country gained strength after a financial crisis in 2002, its economy, the third largest in Latin America, has slowed down in recent years, with GDP growing by only 0.5% last year.
The government is also locked in a battle against American hedge funds who disagree with how is wants to restructure $100bn (£65bn) of debt on which it defaulted in 2001.
While the firms successfully sued Argentina for repayment, Mrs Kirchner refused to pay.
Mrs Kirchner succeeded her husband Nestor as president. He died in 2010, three years after handing over the presidency to his wife.
Mr Scioli, the governor of Buenos Aires province, is a former world powerboating champion who lost his right arm in a boat race in 1989.
Last week, he pledged tax cuts for middle-class workers earning under a certain income, a move expected to affect half a million people.
He has also vowed to bring down Argentina's inflation to single digits in less than four years and promises to introduce policy changes to invigorate the economy.
Like Mr Scioli, Mr Macri is married to a former model. He is a former president of Boca Juniors, Argentina's most successful football club.
The BBC's Wyre Davies, in Buenos Aires, says Mr Macri's centre right coalition Cambiemos - We Can Change - is seen as more market-friendly than Mr Scioli.
While Mrs Kirchner has sought to press Argentina's claims for the disputed UK territory of the Falkland Islands, Mr Scioli says he would not appoint a Falklands minister, and would seek closer ties with London.
"The world is going to watch the new president's first 24 hours very carefully," political analyst Pablo Knopoff told Agence France Presse.
"He'll have to deliver a message to convince people that Argentina is a country where they can invest, with clear rules."