A security official said one bombing targeted an abandoned church in Benghazi which had been previously damaged by fire.
The explosion damaged only a car parked outside and no casualties were reported.
The official said two other explosions targeted parked security vehicles elsewhere in the city.
A soldier was lightly wounded from flying debris.
Tripoli's security spokesman, Essam el-Naas, said two suspects have been arrested for an explosion near the Saudi, Greek and Palestinian embassies. A second went off near a security building.