Voting for the Chowringhee and Basirhat (South) assembly constituencies in West Bengal began at 7 a.m. Saturday.
Chowringhee in Kolkata was won by Trinamool's Sikha Mitra in 2011 assembly polls, where the party fought jointly with the Congress.
The 200,256 electors spread across 222 polling stations have to choose from nine candidates - Trinamool's Nayna Bandyopadhyay, BJP's Ritesh Tiwari, Congress' Santosh K. Pathak, CPI-M's Faiyaz Ahmad Khan and five independents.
The Basirhat (South) constituency is a seat newly carved out in 2011. Nearly 235,843 people are eligible to vote in 286 polling stations.
The BJP has made infiltration from across the Bangladesh border a major issue in this constituency.
After two of its leaders were put behind bars in the multi-crore-rupee chit fund scandal, the ruling Trinamool Congress has come under under fire from its political rivals.