Voting began at 6 am on Wednesday morning amid stringent security arrangements, officials said.
They said the voting would take place at 544 polling stations across the state and would end at 4 pm.
A total of 65 candidates - 61 of them from Kashmir valley - have already won the polls uncontested, while in 56 wards all in the valley - no nomination was received, so no polling is taking place in those places, they said.
As many as 270 polling stations have been designated for voting in Kashmir Division and 274 in Jammu Division, they added.
They said massive security arrangements have been put in place to ensure smooth conduct of the polls.
The elections, covering 79 municipal bodies with an electorate of about 17 lakh, are being held in four phases.
A total of 3,372 nominations have been filed for 1,145 wards. The next phases will take place on October 13 and 16.
The government has declared holiday on the day of poll in the municipal areas concerned to enable voters cast their vote.
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