According to trends made available by the Election Office at 9 AM, an hour after counting began, BJP is leading at Narkatiaganj, Rajnagar (SC), Jale, Hajipur, Banka and Mohania (SC).
RJD is ahead at Chapra and Mohiuddinagar, the EC office statement said.
JD(U) and Congress are leading at Parbatta and Bhagalpur respectively, it said.
The outcome of the bypoll is being considered as a "semi-final" before the crucial state poll next year as it will prove whether regrouping of "Mandal forces" against BJP has paid or not.
Of the 10 seats that went to bypoll, BJP had 6 seats in the 2010 Assembly election while RJD had 3 and JD(U) 1.