Congress was leading in Ajmer and Alwar in the first round of counting, while BJP was leading in Mandalgarh, a poll official said.
In Alwar, Jaswant Singh Yadav of BJP faced Karan Singh Yadav of the Congress, while Raghu Sharma of Congress contested BJP’s Ram Swaroop Lamba in Ajmer.
The main contenders for the Mandalgarh seat were BJP’s Shakti Singh Hada and Congress’s Vivek Dhakad.
In Ajmer, Raghu Sharma from Congress appeared to have set a strong ground in the initial round. He is leading by 8,648 votes.
In Pushkar and Dudu, Congress was leading by 1,500 votes respectively, while in Ajmer north, the party was leading by 3,000 votes. Congress was also leading in Kishangarh.
In Alwar, Karan Singh Yadav was leading by around 10,000 votes, the poll official said.
This is being termed as a crucial contest ahead of the state elections which are scheduled later in 2018.
While the counting of votes for the Alwar and Ajmer Lok Sabha seats was being done in the respective constituencies, the counting for the Mandalgarh assembly seat is being held in Bhilwara.
From Mandalgarh, Hadda was leading by 4,000 votes, the poll official said.
A total of 42 candidates were in the fray for the three seats.
Both the parties have campaigned aggressively, as the bypolls results were expected to reveal the mood for the Assembly polls ahead.
The bypolls were necessitated after the death of BJP MPs Sanwarlal Jat from Ajmer, Mahant Chand Nath Yogi from Alwar, and MLA Kirti Kumari from Mandalgarh.