Electoral officials in Turkmenistan say 95% of voters have cast their ballots to choose a successor to the late president, Saparmurat Niyazov.
The official results are expected on Wednesday
Voters were choosing between six men, in the gas-rich Central Asian nation's first multi-candidate election.
Interim leader Gurbanguly Berdymukhamedov, a former dentist, is seen as the clear favourite.
The government banned exile opposition politicians from standing, drawing international criticism.
Niyazov, who died in December, ruled uninterrupted for 21 years.
The polls closed at 1800 (1300 GMT), with official results expected on Wednesday.
All six of Niyazov's potential successors are members of Turkmenistan's only political party - the Democratic Party - that was created by the late leader.
Gurbanguly Berdymukhamedov is seen a clear favourite
But Mr Berdymukhamedov, the former health minister and the late president's personal dentist, is the clear favourite, the BBC's Central Asian correspondent Natalia Antelava reports.
Even the head of the country's central election commission has publicly vowed to work to ensure Mr Berdymukhamedov's victory.
"We're not voting on the programmes because they are all the same," one Turkmen man told Reuters news agency, as he went to vote.
"Which one promised to pay a pension? That's the one I want to vote for," said an ethnic Russian woman in her 50s.
Like the other contenders, Mr Berdymukhamedov has pledged to follow in the footsteps of the late president.
However, he has also promised unlimited access to the internet, better education and higher pensions.
Only 1% of Turkmenistan's five million people currently have internet access, and the nation's education system is presently based almost entirely on Niyazov's book, Rukhnama.
But after two decades of living under one of the world's most isolated and repressive governments, many voters see this election as a first step towards much needed change, our correspondent says.