The RJD has established a lead in Mokama constituency, while the BJP is ahead in Gopalganj, Election Commission trends revealed after initial rounds of vote counting on Sunday.
In Mokama, Neelam Devi of the RJD is ahead of BJP's Sonam Devi by 12,152 votes.
Kusum Devi of the BJP has taken a lead over Mohan Prasad Gupta of the RJD by 637 votes, EC trends around 11.15 showed.
Of the 6.10 lakh voters - Gopalganj (3.31 lakh) and Mokama (2.70 lakh) 52.3 per cent had exercised their franchise in the two seats on November 3, he said.
A total of 619 polling booths were set up in the two constituencies.
Fifteen candidates are in the fray - nine in Gopalganj and six in Mokama.
This is the first electoral face-off between the ruling Grand Alliance (GA) and the opposition BJP in Bihar after the change of government in August this year, when Chief Minister Nitish Kumar's party JD-U snapped ties with the saffron party and aligned with Lalu Prasad's RJD-led coalition, comprising Congress and other parties, to form a new government.
The Mokama seat fell vacant following the disqualification of RJD MLA Anant Singh after his conviction in an Arms Act case, while the by-election in Gopalganj was necessitated following the death of sitting BJP MLA Subhash Singh.
BJP leader Kusum Devi, wife of the deceased MLA, is pitted against RJD's Mohan Gupta in Gopalganj. In Mokama, BJP nominee Sonam Devi is up against RJD's Neelam Devi, the wife of Anant Singh.
Mokama has been the stronghold of Anant Singh since 2005. He won the seat twice on JD(U) tickets. Singh fought as an RJD candidate in the 2020 elections and retained the seat. But he was disqualified from the assembly following his conviction in the criminal case.