"Polling, which began at 7 AM, has been peaceful so far and 20-25 per cent of votes have been cast till noon in both the constituencies amid tight security," said an official of the Election Commission here.
Counting of votes is on April 13.
The by-poll for Nanjangud (Scheduled Caste) in Myusuru district was necessitated by the resignation of former Congress lawmaker and Revenue Minister Srinviasa Prasad, who is re-contesting on the Bharatiya Janata Party (BJP) ticket.
The ruling Congress has fielded K Keshavamurthy, who lost to Prasad in the 2013 assembly elections as a Janata Dal-Secular (JD-S) nominee. Ten more candidates, including independents are also in the fray.
Mr Keshavamurthy was seen casting vote sporting the party symbol on a shawl he was wearing, which is a violation of the model code of conduct, as he was within 100 metres radius of the polling booth under Section 130 of the Representation of the People Act, 1951.
The by-poll for Gundlupet in the adjacent Chamarajanagar district was caused due to the death of Congress lawmaker and Cooperation Minister HS Mahadeva Prasad on January 2. The ruling party has fielded his widow Geetha against CS Niranjan Kumar of the opposition BJP. Seven more are in the fray.
The JD(S) is not contesting in the twin by-polls as the next assembly elections are due in April 2018.
Nanjangud is about 170 km away from Bengaluru, and Gundlupet 210 km from the state capital.
The poll panel has made elaborate security arrangements for the smooth conduct of polling and to prevent any malpractice.