Bankura and Daspur in the Maoist-hit districts of Jangalmahal and West Midnapur respectively would go to the poll, necessitated by the death of TMC legislators there.
"Security personnel and polling parties, including the presiding officers, have reached the polling stations," state Chief Electoral Officer, Sunil Gupta, told PTI.
While Daspur has an electorate of 2.48 lakh, Bankura has 2.19 lakh voters, he said.
Kashinath Mishra of TMC had won the Bankura seat last year by defeating the CPI(M) by a margin of 29,090 votes while Ajit Bhunia of the TMC had defeated the CPI(M) in Daspur by a margin of about 25,000 votes.
Since both the seats were won by Trinamool Congress last year by big margins, the party is confident of retaining them this time too, notwithstanding the infighting at Daspur over the choice of Ajit Bhuniya's wife Mamata Bhuniya as a candidate from there.
Kashinanth Misra's wife Minati has been fielded as a candidate by TMC in Bankura.
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The CPI(M) has fielded Samar Mukherjee in Daspur constituency and Nilanjan Dasgupta in Bankura seat.
The BJP too, has fielded its candidates in both the seats with Ashok Mal to contest from Daspur and Manisha Chatterjee from Bankura.
However, Congress will not contest the elections.
State Congress vice-president Debabrata Basu told PTI, "We did not put up candidates against the Trinamool Congress as per desire of the Congress High Command."
He claimed that Congress workers did not join the campaign for the TMC candidates "as TMC has not called us for the same."
Chief Minister Mamata Banerjee has not campaigned for her candidates in the two seats and the job was left to her trusted party colleagues including Railway Minister Mukul Roy and state minister for Industry and Commerce Partha Chatterjee.
On the other hand, CPI(M) central committee member and Leader of the Opposition in the Assembly Surya Kanta Mishra had campaigned for both the seats.