They were said to have been targetting recruits as they lined up to enlist for military service to fight against the Houthi insurgency to the north.
One suicide car bomber targeted a line outside the recruitment centre killing at least 20 people.
A second bomber struck on foot as he detonated his explosive vest among a group of recruits waiting outside the home of an army commander, killing at least 25.
Local news website Aden al-Ghad showed pictures of soldiers picking up bloodied comrades in uniform from the ground and witnesses reported seeing ambulances with blaring sirens collecting the wounded from the scene.
The attacks are the latest incident in the increasingly bloody conflict between the Saudi-backed Sunni government in the south against Shia Houthi rebels who control the capital in the centre of country and are allied with the former president.
The chaos has also encouraged activity by affiliates of al-Qaeda and Isis who have stepped up their attacks in a bid to gain a foothold in the country.
More than 6,200 people in Yemen have been killed since the Saudi-led coalition began bombing the country last year.
The war has been condemned by human rights campaginers who say Saudi Arabia is carrying out war crimes against the Yemeni people.
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