The BBC's Jonathan Head says turnout is expected to be very low
Syria has held local elections despite continuing violence between security and opposition forces.
Authorities said the vote had been freer than in previous years, but the opposition called for a boycott and launched a general strike.
Turnout was expected to be very low. Correspondents say many Syrian voters would not risk going to the polls.
Fighting is said to have continued in several cities, with at least 20 people reported killed on Monday.
The Local Co-ordination Committees (LCC), a network of opposition activists, said the deaths had occurred in Idlib in the north, Homs and Hama further south, and in a suburb of the capital, Damascus.
The group said four women and two children were among the dead.
Fierce fighting is also reportedly continuing in the southern province of Deraa.
On Sunday, activists said up to 18 people had been killed across the country - including 11 in Homs and Hama.
The UN estimates that more than 4,000 people have died in the nine-month uprising, including 307 children.
The Syrian government says it is fighting armed groups. Many army defectors have joined the opposition in recent months.
Reports from Syria are difficult to verify as foreign journalists are unable to move around the country freely.
War zoneThe Syrian state news agency reported people flocking to polling stations.
But in opposition strongholds activists said there were few signs that an election was even happening, and almost no-one was voting, reported the BBC's Jonathan Head in neighbouring Turkey.
In these places shops remained shut on the second day of an indefinite general strike called by the opposition, reports say.
The authorities said Monday's polls were part of reforms being introduced in response to the protests.
"The new election law contains the necessary guarantees for a democratic, transparent and honest election," the head of the elections committee, Khalaf al-Ezzawi, told state media.
About 43,000 candidates have been competing for more than 17,000 seats in local councils across Syria.
Zeina, a voter in Damascus, told AFP news agency: "I voted because we want to contribute to the reforms " pledged by President Bashar al-Assad.
But our correspondent says the vote means little in much of the country, where going out to cast a ballot can be too dangerous.
He says Homs - Syria's third-largest city - resembles a war zone, with gun battles occurring every day between army units and lightly armed opposition forces.
A resident of the city told the Arabic news channel al-Jazeera: "I didn't even know an election was taking place.
"The people of Homs have removed every picture of Bashar al-Assad from the streets, so don't expect to see pictures of candidates who are no more than stooges of the regime."
Foreign pressureThe opposition Syrian National Council (SNC) has warned of an impending final assault on Homs by security forces.
It also said that the general strike launched on Sunday was being widely observed in 12 provinces.
President Assad is under international pressure to end the continuing crackdown on anti-government protesters.
United Nations Human Rights Commissioner Navi Pillay is due to brief the Security Council on the situation in Syria later on Monday.
On Saturday, the Arab League is due to discuss Damascus's conditional acceptance of the league's plan to send in monitors to assess the violence.
Last month the league suspended Syria's membership in protest at the continuing crackdown and also imposed economic sanctions.
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