The ruling Janata Dal (United) and the BJP are facing a Congress and Rashtriya Janata Dal combine in all the three battles.
In Araria parliamentary constituency, seven candidates are fighting it out. Former BJP parliamentarian Pradeep Kumar Singh is hoping to wrest the seat from the RJD, which has fielded Sarfaraz Alam, whose father Mohd Taslimuddin was a parliamentarian from this seat. Mr Taslimuddin's death necessitated the by-election on this seat.
In Jehanabad, the RJD hopes to retain the assembly seat that fell vacant after the death of Mundrika Yadav. Mr Yadav's son Kumar Krishna Mohan is contesting from this seat.
Though fourteen candidates are in the fray in Jehanabad, the fight is mainly between the RJD's Kumar Krishna Mohan and JD(U)'s Abhiram Sharma, who took the seat in the 2010 assembly election.
The results will be out on March 14.
The Bihar by-election is the first electoral battle in the state since last year's realignment when Chief Minister Nitish Kumar, who also heads the JD(U), left the Grand Alliance and reunited with the BJP.