At 9 a.m. about 12.8 per cent polling was logged at Vikravandi, while at Nanguneri it was about 18 per cent.
Polling began at 7 a.m. and would conclude at 6 p.m. The counting of votes would be taken up on October 24.
A total of 35 candidates are in the fray in both the seats.
The bypoll in Vikravandi was necessitated following the death of DMK Legislator K. Rathamani in June, while the Nanguneri seat fell vacant as Congress Legislator H. Vasantha Kumar resigned after he got elected to the Lok Sabha.
A total of 23 candidates are in the fray in Vikravandi seeking the favour of about 2.24 lakh voters.
The main fight is between ruling AIADMK's R. Muthamilselvan and the principle opposition party DMK's N. Pugazhenthi.
On the other hand, Nanguneri seat will see 12 candidates fighting it out though the main rivals are AIADMK's V. Narayanan and Congress candidate Ruby R. Manohar.
The total number of voters in Nanguneri is about 2.57 lakh.
The security has been beefed up in the two constituencies for the peaceful conduct of the polls.
Leaders of the AIADMK, DMK, Congress and other parties campaigned for their own candidates as well as for the candidate of their allies.
For the ruling AIADMK, the campaign was spearheaded by Chief Minister K. Palaniswami, Deputy Chief Minister O. Panneerselvam, State Ministers and others.
On the other hand, for the DMK the campaign was led by party President M.K. Stalin and others.
The leader of the Naam Tamilar Katchi, Seeman created a controversy while campaigning for his party candidate in Vikravandi justifying the gruesome killing of Rajiv Gandhi for sending the Indian Peace Keeping Force (IPKF) to Sri Lanka.
During his campaign 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 Tamil was later murdered in the Tamil land.
A female Tamil Tiger suicide bomber blew herself up at an election rally near Chennai killing the former Prime Minister on 21.5.2991.
Seeman was booked by Tamil Nadu police for his provocative speech with an intention to cause riots and intentional insult to breach the 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.
( With inputs from IANS )