In Bongaon, Trinamool candidate Mamatabala Thakur was ahead of her nearest rival Subrata Thakur of the BJP in all the seven assembly segments after the first round of counting.
CPI-M nominee and former state minister Debesh Das, who had finished runners-up in the 2014 Lok Sabha elections, was at third position. Congress candidate Kuntal Mondal was fourth.
The by-poll was necessitated by the death of Trinamool MP Kapil Krishna Thakur.
In Krishnaganj of Nadia district, Trinamool candidate Satyajit Biswas was leading by 8645 votes over his closest rival Apurba Biswas of the CPI-M.
BJP nominee Manabendra Roy and Nityagopal Mondal of the Congress were in the third and fourth positions respectively.
The seat became vacant due to the death of Trinamool lawmaker Sushil Biswas.
Over 80 percent voters cast their franchise on Feb 13 for the two seats.