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.
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.
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