Turnout was reported to be moderate, and the results are due on Sunday.

The BBC's Satish Jacob: "Most voters realise there is not much to differentiate one party from another"

Correspondents say the campaign was dominated by economic worries - symbolised by the soaring price of onions - with the two main parties trying to pin the blame for the situation on each other.

The results - in Delhi, Madhya Pradesh, Mizoram and Rajasthan - will have no direct bearing on the federal government.

Young children at a Congress Party rally

But with the opposition Congress Party hoping to stage a comeback, correspondents say substantial sebacks for the nationalist BJP (Bharatiya Janata Party) of the prime minister, Atal Behari Vajpayee, could encourage defections from his coalition.

The latest opinion polls predict sweeping victories for the opposition Congress Party, headed by Italian-born Sonia Gandhi, in Delhi city and the desert state of Rajasthan, both ruled by the governing Bharatiya Janata Party (BJP) of the Hindu nationalists.

Congress is also expected to retain the state of Mizoram, while the BJP stands a good chance of winning back Madhya Pradesh.

Correspondents say, however, that polls are not always reliable, particularly in areas of large poor and illiterate communities.

BJP supporters wearing the party's colours - soaring prices have affected many

Prime Minister Atal Behari Vajpayee has dismissed speculation that defeats for the BJP could lead to the opposition toppling the government in the national parliament.

"There is no question of the Congress [Party] being able to form an alternative government," Mr Vajpayee told reporters.

"The results of these elections will not change ground realities ... We are in a majority ... and there will be no problem," Mr Vajpayee said.

But a senior BJP official admitted that the party was feeling vulnerable.

Local elections, national issues

The BBC's India correspondent, Daniel Lak says that these essentially local elections have been fought largely on national issues, particularly food prices, which have been soaring recently.

Precious commodity - the price of onions has risen eight-fold

The Congress Party has adopted the onion - one of the staples most affected by inflation - as a symbol: its price has jumped six to eight times in less than a year's time.

Even in the central Indian state of Madhya Pradesh, where the Congress Party is in power, the campaign has been largely about the central government's handling of the economy.

The parties have also accused each other of corruption.

Congress Party President Sonia Gandhi accused the BJP of failing to control prices and crime, and of overturning a decades-old political consensus on foreign and defence policies.

Prime Minister Atal Behari Vajpayee, who acted as the BJP's star campaigner, countered that decades of misrule by the Congress Party was responsible for many of India's ills.