They said the bombings targeted young men seeking to join the army.
One suicide car bomber targeted a line outside an army recruitment center, killing at least 20. A second bomber on foot detonated his explosive vest among a group of recruits waiting outside the home of an army commander, killing at least 25.
Scores of others were wounded, said the officials, who spoke on condition of anonymity because they were not authorised to brief the media.
Yemen has for nearly two years been gripped by a war pitting the internationally recognized government against Shiite rebels who control the capital, Saana, and are allied with forces loyal to a former president.
No one claimed responsibility for Sunday's attacks, which bore all the hallmarks of Islamic militants.
Monday's blasts underline the precarious security situation in Aden, the country's main port on the Arabian Sea, several months after government forces and allied militiamen backed by a Saudi-led coalition retook the city from the Shiite rebels, also known as the Houthis.
The city has in recent months seen a series of suicide bombings and assassinations mainly targeting army and security forces. Contributing further to the instability in Aden is recent the eviction of northern Yemenis, the work of suspected separatists who seek an independent south.
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