While one of the blasts took place near the house of All India United Democratic Front (AIUDF) legislator from Jaleswar constituency Mainuddin Ahmed, the other one occurred in Gaurnagar area in the Golapara district.
A youth was beaten to death by angry residents of Jaleswar Saturday night for allegedly triggering the blast.
Police had also recovered a low intensity crude bomb from Jaleswar area later.
Assam Police IGP (Law and Order) S.N. Singh confirmed the blasts.
"These are very low intensity blasts. We are trying to trace the militants involved behind it," he said.
An alert had been sounded across Assam last week following intelligence reports that anti-talk faction of the Ulfa might try to disrupt the Republic Day celebrations in the state.
The Republic Day celebrations was, however, passed off peacefully without reports of any untoward incident.