People in the hill state have been alternating between the Congress and the BJP in assembly elections every five years.
The Times Now-VMR and Zee News-Axis exit polls predicted that the BJP would win 51 of the total 68 assembly seats in the state.
While the Times Now-VMR exit poll gave 16 seats to the Congress and one to another, the Zee News-Axis poll gave 17 seats to the party in power in Shimla.
There are a total of 68 seats in Himachal Pradesh, elections to which were held on November 9. A party needs 35 seats to be able to form a government.
The final results will be out on December 18.
The Aaj Tak-Axis exit poll gave 47-55 seats to the saffron party, 13-20 to the Congress and 0-2 to others.
Among other exit polls, the News X survey predicted that the BJP would win 42-50 seats and the Congress, 18-24.
In the 2012 election, the Congress came to power by winning 36 seats, while the BJP got 26 seats and others bagged the remaining six.