An explosives-rigged vehicle blew up in front of a mosque in the central neighbourhood of Al-Sleimani, a security source said.
A second car exploded 30 minutes later in the same area, causing more casualties among security services and civilians, the source added.
The mosque is known to be a base for Salafist groups which fought jihadists in the eastern port city alongside forces loyal to military strongman Khalifa Haftar.
Fadia al-Barghathi, a spokeswoman at the city's Al-Jala hospital, said the attacks had caused 43 casualties, including the deaths of nine people.
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Military strongman Khalifa Haftar in July announced the "total liberation" of Benghazi, three years after his forces launched a military operation to seize the city from jihadists who had made it a stronghold following the revolution.
But clashes and attacks in the city have continued, including against diplomatic facilities and security forces.
Haftar supports a parliament based in the far east of Libya, while a rival United Nations-backed unity government in the western capital Tripoli has struggled to assert its authority nationwide.