Rabri Devi, RJD vice-president, filed her nomination papers at the Assembly secretariat in presence of her sons Tej Pratap Yadav and Tejashwi Yadav, and other leaders.
Hindustani Awam Morcha's Santosh Manjhi, son of party chief and ex-chief minister Jitan Ram Manjhi, too filed his nomination papers.
The HAM recently switched over from the NDA to the RJD-led Grand Alliance.
The elections will be held in 11 seats which fall vacant next month in view of the expiry of terms of the sitting members.
The JD(U), headed by the chief minister and its ally, the BJP, are yet to come up with names of their candidates.
The Congress, which is an RJD ally, is also likely to field a candidate as it currently has the requisite number of MLAs to get a member elected to the Council.
The last date of filing of nomination papers is April 16.
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