Here are the latest developments:
A voter turnout of 51.1 per cent was recorded till 3 pm in the Maoist-affected districts of Kaimur, Rohtas, Arwal, Jehanabad, Aurangabad and Gaya.
Voting ended at 3 pm in 11 constituencies and at 4 pm at 12 others because of security concerns. In only nine seats voting was held till the usual 5 pm.
Of the 32 seats where polling was held today, 19 were won last time by the Janata Dal (United) and 10 by the BJP, who were partners in 2010. This time, the two parties are leading rival camps.
Jitan Ram Manjhi, former Bihar chief minister and now BJP ally, is the man to watch in this phase. He is contesting two seats - Imamganj where he takes on Uday Narain Chaudhary of the JD(U), Speaker of the outgoing assembly and a five-term legislator from the seat.
Mr Manjhi, who launched his own party Hindustani Awam Morcha (HAM) earlier this year after being thrown out of the JD(U), is also contesting from Makhdumpur seat in Jehanabad too.
Bihar Chief Minister Nitish Kumar, seeking a third straight term, is leading the "Grand Alliance" that includes Lalu Prasad's RJD and the Congress. He takes on the BJP, which has partnered with Mr Manjhi and two other regional parties.
The first phase of polling on Monday, saw a record voter turnout at 57 per cent. More women voted in the first phase - 59.5 per cent - than men - 54.5 per cent.
Elections in the state are being conducted in five-phases. Votes will be counted on November 8.