The first bomb exploded in a crowded market in the heart of Guwahati, killing five people, police said on Sunday.
Ten others were wounded, three of whom later died in hospital.
Police said the bomb exploded in front of a sweet shop in the Fancy Bazar area of Guwahati, the main city of Assam state.
A second bomb went off outside an oil installation on the outskirts of the city killing two people.
Three others were injured in that explosion.
Nitul Gogoi, a senior police officer, said: "Both the bombs were powerful and we are yet to identify who is behind this incident."
Assam has been home to a nearly 30-year-old insurgency led by the United Liberation Front of Asom (ULFA) which is fighting for an independent homeland. Tens of thousands of people have died in the revolt.
The ULFA and the Indian government called off peace talks in September after New Delhi ended a truce with rebels.
Violence has since increased in the oil and timber rich region.