The bye-elections are being held for Araria Lok Sabha seat and, Jahanabad and Bhabhua Assembly constituencies.
According to election commission sources, the polling is so far peaceful.
In Araria parliamentary constituency, seven candidates are in the fray. Former BJP MP Pradeep Kumar Singh is seeking to regain the seat from the RJD which has fielded Sarfaraz Alam, the death of whose father Mohd Taslimuddin has necessitated the bypoll.
A total of 14 candidates are in the fray though the contest is mainly between the RJD nominee and JD(U)'s Abhiram Sharma who had won the seat in the 2010 Assembly polls.
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The BJP is hopeful of retaining the Bhabhua Assembly seat riding on a sympathy wave for Anand Bhushan Pandey whose death at the age of 48 has necessitated the bypoll.
The saffron party has fielded Pandey's wife Rinky Rani and her principal challenger is Congress candidate Shambhu Singh Patel. The total number of candidates in the fray here is 17.
The bye-elections are being watched with much eagerness as this is the first electoral battle in the state since last year's political realignment when Chief Minister Nitish Kumar, who also heads the JD(U), walked out of the Grand Alliance and rejoined the BJP-led NDA.