Blasts and road blockades carried out by Maoists disrupt polls in Chattisgarh.
More than 30 people who called for a boycott have been detained in recent days under legislation that allows police to hold people for up to two years without trial.
The detainees were held for advocating “secession, breach of the peace and intimidating people not to vote”.
B Srinivas, a senior police official, said: “We will not allow anybody to campaign against the elections.”
Mirwaiz Umar Farooq, a key separatist leader who has been under house arrest for three days, condemned the vote.
“You can’t have free and fair elections in the presence of hundreds of thousands of occupying forces,” he said.
Paramilitary soldiers and police officers outnumbered voters as polling stations opened in towns north of the summer capital city Srinagar.
“The way the government suppressed recent demonstrations has put me off and I am not participating in the elections now”
Mohammed Abdullah, vegetable seller, Srinagar
The elections are being held in seven phases in Jammu and Kashmir between November 17 and December 24 – partly because of security issues.
Police fear there will be further outbreaks of unrest, although separatist leaders say they will not use violence to enforce the boycott call.
The boycott is expected to be widely supported, particularly in the wake of the recent demonstrations which were the largest pro-independence protests across Kashmir for two decades. At least 48 people died in the unrest, many of them shot dead by police.
Mohammed Abdullah, a 55-year-old vegetable vendor in Srinagar, said: “I have always voted in the past elections, but the way the government suppressed the recent demonstrations has put me off and I am not participating in the elections now.”
Prem Shankar Jha, former editor of Hindustan Times and author of Kashmir 1947: The Origins of a Dispute, does not believe there will be much violence “simply because the groups are now united”.
However, he told Al Jazeera: “The government will be lucky if they get more than 10 per cent of people to come out and vote … 15 per cent is the likely maximum turnout.”
Anti-Indian sentiment is widespread across Kashmir, where most people favour either independence or allegiance with neigbouring Pakistan.
Jha predicts that even if the polls pass without incident, the bigger challenge will be to persuade the local population – whether they are in favour of independence or secession to Pakistan – that the election has legitimacy.
“In a sense, they [Kashmiris] feel they have been manhandled by Delhi. It is about disempowerment, they are rebelling against that disempowerment,” he said.
The final count for the state is expected on December 28.
The other five states due to go to the polls over the next few weeks are Madhya Pradesh, Rajasthan, Mizoram and New Delhi.