The first bombing happened in the central city of Homs at 7.14 a.m, when an explosive-laden vehicle was detonated at the checkpoint when it was detected by military personnel, Xinhua news agency reported.
Four people were killed and many injured in the explosion.
Some 30 people were killed and many injured in Tartus city, in twin-bombings that rocked a checkpoint at the city's entrance.
Both bombers, wearing military uniforms, were disguised as government troops, the military said.
An explosive-packed motorcycle exploded in the predominantly-Kurdish city of Hasakah, killing eight persons.
The Islamic State claimed responsibility for the Hasakah bombing, saying it targeted a checkpoint of the Kurdish security forces, known as Assayish.
An explosion on a road between the resort town of Sabura and Bajaj killed one person.
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