Turkmenistan is of substantial interest to Russia and the West because of its enormous natural gas reserves, and its status as a stable, neutral country bordering Iran and Afghanistan.
The state Turkmen Press news agency called the vote "a true national holiday" that demonstrated "Turkmens' civil maturity."
Berdymukhamedov and his five opponents are all members of the country's only legal political party and were appointed by the People's Assembly, the highest legislative body, which is scheduled to meet on Wednesday to endorse a winner.
The Organisation for Security and Cooperation in Europe did not send an election-monitoring mission, nor did the Commonwealth of Independent States, a loose grouping of former Soviet republics.
Goran Lennmarker, chairman of the OSCE Parliamentary Assembly, said that the vote was "a step ... in the development of democracy."
"You've had a very strong leader. Now this is a new step in your development," he said.
Exiled opposition figures have not been able to return to Turkmenistan since Niyazov's January 21 death, and many foreign journalists were denied visas to cover the election.
Cult of personality
Shortly after midday on Sunday, a group of locally accredited journalists who were being taken to polling stations were told to go home and wait for official statements.
Niyazov fostered an extensive personality cult, calling himself Turkmenbashi, or 'Father of all Turkmen', still dominates the country's psyche nearly two months after his death.
At a polling station in Niyazov's hometown of Kipchak, his portrait was on all the walls, and copies of his poems and philosophical writings were on display.
First-time voters were being given copies of the "Rukhnama," a book of Niyazov's philosophical writings, which he made required reading in schools. Niyazov said the book would guarantee diligent readers a place in heaven.
| Berdymukhamedov is the |
clear favourite [EPA]
Berdymukhamedov, by contrast, has kept a fairly low profile.
He ceded his allotted television campaign time to the other candidates, state TV has shown only briefly shown his remarks, and his photo is rarely displayed in state newspapers.
He also startled observers with a series of remarks indicating a significant move away from Niyazov's tight control.
He promised unrestricted internet access for all Turkmens, support for entrepreneurship, social reforms and a widening of educational opportunities.
Ganid Agayev, a retiree in Ashgabat, said he voted for Berdymukhamedov because of his statements about education.
"This has raised my spirits. I have grandchildren, and it's very important for me that they get a proper education," he said.
Amanjan Khojiyeva, another retiree, said she voted for Berdymukhamedov because he promised to raise pensions.
But Berdymukhamedov, who also holds the title of deputy prime minister, has not spoken of political reform. He promised the country would follow democracy, as Niyazov defined it.
Berdymukhamedov, a dentist by training, emerged as acting president after the arrest on criminal charges of the speaker of parliament, who under the constitution was to take over in case of the president's death.
Preliminary election results are expected on Tuesday.