Polling began at 7 a.m. and will conclude at 6 p.m. The counting of votes will be held on October 24.
The bypoll in Vikravandi was necessitated following the death of DMK Legislator K. Rathamani in June, while the Nanguneri seat fell vacant after Congress Legislator H. Vasantha Kumar got elected to the Lok Sabha and resigned.
A total of 35 candidates are in the fray in the two seats.
In Vikravandi, some 23 candidates are seeking favour from about 2.24 lakh voters.
The main fight is between the ruling AIADMK's R. Muthamilselvan and DMK's N. Pugazhenthi.
In Nanguneri, about 2.57 lakh voters will decide the fate of 12 candidates, though the main fight is between the AIADMK's V. Narayanan and Congress candidate Ruby R. Manohar.
While campaigning for his party candidate in Vikravandi, Naam Tamilar Katchi (NTK) leader Seeman started a controversy when he justified former Prime Minister Rajiv Gandhi's gruesome killing for sending the Indian Peace Keeping Force (IPKF) to Sri Lanka.
Seeman said history will be rewritten in the future to the effect that Rajiv Gandhi, who had sent the IPKF to Sri Lanka to kill Tamilians, was later murdered in the Tamil land.
A female suicide bomber of the Liberation Tigers of Tamil Eelam (LTTE) blew herself up at an election rally near Chennai killing the former prime minister on May 21, 1991.
Seeman was booked by the Tamil Nadu police for making the provocative speech with the intention to cause riots and breach of peace.
In the 234-member Tamil Nadu Assembly, the ruling AIADMK has 123 members (including the Speaker), DMK-100, Congress-7, IUML and Independent have one each and two seats are vacant.