Only the centre-left has held a primary in France so far, the one organised by the Socialist Party in 2011.
Now the mainstream right Republicans have organised one, with small centrist and right-wing parties participating, ahead of the 2017 presidential election.
Primaries à la française
The idea is imported from the US but a French touch has been added - as in national elections, there are two rounds, allowing voters whose favoured candidate has been squeezed out in the first round to pick a second best in the decider.
And voters do not have to register with a party, all they have to do is pay two euros and sign a declaration of loyalty to the "values of the right and the centre".
That has led some left-wing voters to consider registering and voting for Juppé to stop Sarkozy winning, especially since all opinion polls show the final round of the presidential poll being between the mainstream right and Marine Le Pen of the far-right National Front (FN).
Voting actually began on Saturday overseas but in mainland France participants have to turn up to one of 10,228 polling stations, mostly in city halls and schools, to cast their ballot.
Who is standing?
The seven candidates are:
Alain Juppé, 71, mayor of Bordeaux, former prime minister, foreign minister and defence minister;
Nicolas Sarkozy, 61, former president and interior minister, who lost the 2011 election and rebranded what was then the UMP as the Republicans, faces several legal investigations, including accusations that his 2004 election campaign received funding from Moamer Kadhafi's Libya;
François Fillon, 62, former prime minister (under Sarkozy), MP for a Paris constituency;
Bruno Le Maire, 47, former agriculture minister (under Sarkozy), the youngest candidate, MP for a constituency in the Eure, Normandy;
Nathalie Kosciusko-Morizet, 43, former environment minister (under Sarkozy), MP for a constituency in Essonne near Paris, fired as vice-president of the Republicans by Sarkozy after criticising him, failed to win Paris mayoral election, the only woman candidate;
Jean-François Copé, 52, mayor of Meaux, former budget and interior minister, MP for a constituency in Seine et Marne, east of Paris, won the presidency of the UMP after a rancorous campaign against Fillon but over an election funding scandal that also affects Sarkozy;
Jean-Frédéric Poisson, 53, leader of the Christian Democratic Party, MP for an constituency in the Yvelines, near Paris, the only candidate not a Republicans member.
What do they stand for?
All the candidates agree on ending the 35-hour week, raising the retirement age and cutting public expenditure, although not necessarily on how quickly these tasks should be accomplished.
Fillon has risen dramatically in opinion polls this week, especially after the last TV debate, in which he refused an invitation to attack his rivals personally.
The main political debate has been between Juppé and Sarkozy over the place of Muslims and immigrants in French society and the state's response to terrorism.
Alain Juppé: Wants a "happy identity", accusing Sarkozy of adopting far-right policies and declaring "I will always refuse to exploit fear and appeal to base instincts", will not try to change or repeal the Socialist government's same-sex marriage law but will repeal payment of income tax at source, which is currently going through parliament;
Nicolas Sarkozy: Says he stands for the "silent majority", wants the burkini banned, rights of immigrants' families to join them in France curtailed, "assimilation" not "integration" of immigrants, declaring that when one takes French nationality "one lives like a French person and our ancestors are the Gauls", has taken conflicting positions on same-sex marriage, finally opposing repeal;
François Fillon: Very pro-free market, wants to cut 500,000 civil service jobs and reduce immigration to the "strict minimum", said that Donald Trump's election as US president should lead Europe to review its relations with Russia;
Bruno Le Maire: Published a 1,012-page "presidential contract" proposing referendums on modernising political life and reforming the EU, cuts in social security benefits and 80 billion euros in cuts in spending, including axing 500,000 civil service jobs, is concerned that "my intelligence is an obstacle";
Nathalie Kosciusko-Morizet: Attacked Sarkozy for hinting at scepticism about climate change and Poisson for being too friendly to the National Front but declared that "we cannot take in" economic refugees at the moment, in favour of same-sex marriage and assisted procreation for gay couples;
Jean-François Copé: Wants a "right without inhibitions", has talked tough on Islam and immigration on several occasions, famously does not know the price of a pain au chocolat pastry;
Jean-Frédéric Poisson: Wants same-sex marriage law repealed, wants the number of abortions reduced, considers Islam a "danger to our country today" but opposes banning the burkini, refused to rule out voting for Le Pen if she faces Hollande in the second round of the presidential election.
How many will vote?
Campaigning ended on Friday night with Juppé, Sarkozy and Fillon rallying their supporters in Lille, Nîmes and Paris respectively.
Nobody had any idea how many people would vote on Sunday - three million voted in the left-wing primary in 2007 and more than five million people watched the final debate between the right-wing hopefuls on Thursday night.