Congress' Kalale N Keshavamurthy was leading by over 15,000 votes against former Minister V Srinivas Prasad of BJP in Nanjangud.
In Gundlupet, Geeta Mahadeva Prasad (Cong) was ahead by over 4,500 votes against BJP's C S Niranjanakumar, electoral officials said.
Both the seats were held by the Congress.
bypolls were necessitated in Gundulpet following the death of Cooperation Minister Mahadeva Prasad and in Nanjangud due to the resignation of Srinivas Prasad as Congress MLA after he was dropped from the ministry.
Former Prime Minister H D Deve Gowda's JD(S) had not fielded its candidates.