Voters in France have been choosing between Francois Fillon and Alain Juppe to be their centre-right presidential candidate in next year's election.
Mr Fillon is now seen as the favourite to win Sunday's run-off, after securing 44.1% of votes in the first round a week ago. Mr Juppe had 28.5%.
Former President Nicolas Sarkozy was knocked out of the race.
The Republican candidate is widely expected to take on far-right National Front leader Marine Le Pen next spring.
Polls across France closed at 18:00 GMT, with the results expected in the coming hours.
It is the party's first such primary vote, modelled on the US system. The race for the nomination has come down to a choice between two former prime ministers.
Turnout on Sunday appears to be higher than in the first round a week ago, when more than four million people cast their ballots.
Thierry Solere, president of the organising committee, said the number of voters was 4.5% higher at 17:00 local time (16:00 GMT) on Sunday than at the same time in the first round, with 78% of polling stations taken into account.
Both Mr Fillon, 62, and Mr Juppe, 71, want economic reforms - but they differ widely on how far and how fast to take them.
Mr Fillon says France is angry and wants radical change. He is planning to slash 500,000 public jobs.
Mr Juppe is proposing to sack just over half that number of people, and is focusing on a message of harmony and diversity.
Earlier this week, the two contenders clashed over the level of change they were promising to bring in a TV debate.
A poll of 908 debate viewers by Elabe suggested 71% of conservative respondents found Mr Fillon more convincing, as did 57% of viewers of all political stripes.
Analysis - Hugh Schofield, BBC Paris Correspondent
Nothing is certain.
There are many people on the centre and left of French politics who think Francois Fillon is too right-wing and that he has less of a chance than Alain Juppe of beating Marine Le Pen in the presidential election.
These Fillon-sceptics are allowed to vote in the primary, which is open to all voters - and if they do so in numbers, it could make a difference.
Mr Juppe - who was once the favourite to win this primary - has spent the past week highlighting Mr Fillon's personal views on abortion and gay marriage, which is widely seen as a bid to mobilise centrist and perhaps even left-wing voters, the BBC's Lucy Williamson in Paris reports.
Mr Juppe also said his rival was close to Russian President Vladimir Putin, amid growing tensions between the West and Moscow over the crises in Syria and Ukraine.
"This must be the first presidential election in which the Russian president chooses his candidate," Mr Juppe said.
Mr Fillon has argued that the EU and the US "provoked" Russia by expanding in Eastern Europe, calling for an alliance with Russia to fight Islamic State militants in Syria.
Mr Fillon, a Roman Catholic, has also complained of being portrayed as a "medieval conservative", describing his opponent as a "man of the system" with no real plans for change.
After losing last Sunday's first round, Mr Sarkozy endorsed Mr Fillon.