Votes are being counted after Chechnya's first parliamentary poll since Moscow restored control in the region in 1999.
Some 24,000 police and troops were deployed for the polls
Turnout was 57%, election commission Chairman Ismail Baikhanov told Itar-Tass news agency. Voting was held under heavy security.
Moscow says the election proves that Chechnya is returning to normality after more than a decade of conflict.
But separatists and human rights groups have dismissed the vote as a farce.
The BBC's Steve Rosenberg in Chechnya says the polling stations he was able to visit were memorable for their absence of voters and for the presence of armed guards.
At one voting centre in the capital, Grozny, a policeman was overheard whispering to another policeman: "There have been more journalists here today than voters."
However officials say the threshold of 25% needed to make the vote valid was reached early in the day.
The first results are expected later on Monday.
Some 350 candidates are competing for 58 seats. Eight Russian parties are fielding candidates, while independents are also standing.
Observers from Russia, the Arab League and the Organisation of the Islamic Conference are monitoring the vote.
Since the rebels were ousted, Chechens have voted for a new constitution, enshrining the region's status as part of Russia, in a vote widely seen as flawed.
In another controversial vote, they elected Mr Alkhanov, and now voters are being asked to choose MPs, most of whom are expected to be loyal to the Kremlin.
UK-based Chechen rebel envoy Akhmed Zakayev dismissed the vote as "pseudo-elections".
The UK's Lord Judd, a former Council of Europe special rapporteur on Chechnya, said this week that the election was based on flawed premises.
"I simply do not believe we will have stability, peace and a viable future for the Chechen people until we have a real political process," he said.