BBC
Turnout is expected to be very low. Correspondents say many Syrian voters will not risk going to the polls.
Fighting is said to be continuing in several cities, with at least 13 people reported killed on Monday.
The Local Co-ordination Committees (LCC), a network of opposition activists, said the deaths had occurred in three restive regions - Idlib in the north and Homs and Hamas further south.
The group said four women and two children were among the dead.
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 zone The Syrian state news agency reports people flocking to polling stations.
The uprising against Syria's regime shows no sign of abating But in opposition strongholds activists say there are few signs that an election is even happening, and almost no-one is voting, reports the BBC's Jonathan Head in neighbouring Turkey.
In these places shops remain shut on the second day of an indefinite general strike called by the opposition, reports say.
The authorities say Monday's polls are 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 are 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 pressure The 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.
The BBC's Jonathan Head says turnout is expected to be very low
Syria is holding local elections despite continuing violence between security and opposition forces.
Authorities said the vote would be freer than in previous years, but the opposition has called for a boycott and launched a general strike.Turnout is expected to be very low. Correspondents say many Syrian voters will not risk going to the polls.
Fighting is said to be continuing in several cities, with at least 13 people reported killed on Monday.
The Local Co-ordination Committees (LCC), a network of opposition activists, said the deaths had occurred in three restive regions - Idlib in the north and Homs and Hamas further south.
The group said four women and two children were among the dead.
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Homs residentI didn't even know an election was taking place”
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 zone The Syrian state news agency reports people flocking to polling stations.
The uprising against Syria's regime shows no sign of abating In these places shops remain shut on the second day of an indefinite general strike called by the opposition, reports say.
The authorities say Monday's polls are 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 are 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 pressure The 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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