Today's vote is the first stage in a three-part election to select representatives at the district, municipal and regional levels.
The vote has been dismissed by Syria's central government as "a joke", but for Kurds it represents a step towards a long-sought federal system.
Kurds made up around 15 per cent of Syria's pre-war population and were long oppressed by the central government.
But they largely stayed out of the uprising that erupted in March 2011, instead quietly building local control in Kurdish-majority areas after the withdrawal of most government troops.
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Elections for executive councils for towns and larger areas are planned for November 3.
Then, on January 19, a final phase will elect legislative councils for each of the three regions, as well as a single joint legislative assembly.
At a polling station in Qamishli, in the northwestern province of Hasakeh, men and women, young and old, waited to vote, some eagerly brandishing their light blue voting cards.
They pressed their fingers into ink to fingerprint the cards, and then voted behind a curtain before placing their ballots in envelopes and into transparent boxes.
A portrait of Abdullah Ocalan, the leader of Turkey's outlawed Kurdistan Workers Party (PKK) who is jailed in Turkey, hung in the voting room in one polling station.
Voter Mohamed Khalil said the election was the realisation of a dream for Syria's Kurds.
"Before, we were foreigners deprived of the right to run in elections and vote," the man told AFP, his grey hair and moustache neatly groomed.
"We didn't know the meaning of freedom, and we didn't have any rights. Today, and for the first time, we have been allowed to vote and stand, and we know the meaning of freedom."
Syrian Kurdish leaders say they do not want independence, but rather seek a federal system that protects their rights.
But Turkey has been angered by what it sees as twin bids for autonomy by Syria and Iraq's Kurdish populations.
Qamishli resident Abdel Karim Haj Daoud, dressed in a white traditional robe, described today's vote as "like a referendum for us".
"People are happy and optimistic, as you can see there is a lot of congestion and high demand at the ballot boxes," he told AFP.
Small parties allied to the PYD are also running but other local opposition groups are not participating in the vote.
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