The byelections were necessitated due to the death of incumbent BJP MLAs Mukta Tilak (Kasba) and Laxman Jagtap (Chinchwad).
These polls pitted the BJP and Eknath Shinde-led Shiv Sena against the Maha Vikas Aghadi (MVA) alliance of the Congress, Nationalist Congress Party (NCP) and Shiv Sena (Uddhav Balasaheb Thackeray).
The main contenders in the Kasba constiutency, located in the old area of Pune city, are Hemant Rasane of the BJP and Ravindra Dhangekar of the Congress (backed by the MVA).
In Chinchwad, an industrial town near Pune, the fight is between Ashwini Jagtap of the BJP, Nana Kate of the NCP and independent Rahul Kalate.
The Kasba bypoll counting was being held at the Food Corporation of India warehouse in Koregaon Park, while that for Chinchwad Assembly seat was underway at Shankarao Gawade Kamgar Bhavan in Thergaon, the official said.
There would be 20 counting rounds for the Kasba seat and 37 rounds for the Chinchwad seat.
Heavy police security has been deployed at the counting centres.