One attacker drove his bomb-laden truck into a checkpoint in a western district of Hadramawt's provincial capital Mukalla, security officials told AFP.
The second attacker simultaneously blew up his vehicle at an army checkpoint in the nearby town of Hajr, some 15 kilometres (nine miles) to the west of Mukalla, the sources said.
Al-Qaeda in the Arabian Peninsula claimed responsibility for the two attacks in a report on its Telegram account.
AQAP said "dozens were killed and wounded" from forces loyal to President Abedrabbo Mansour Hadi and it posted photographs of the two bombers.
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Eleven people were killed and 18 were wounded in the twin bombings, said Riad Jariri, head of the health department in Mukalla.
Four civilians were among those killed, he told AFP.
Mukalla and surrounding towns were under the control of AQAP for one year until pro-government troops backed by a Saudi-led coalition recaptured the city in April.
In March, a US air strike on an Al-Qaeda training camp in Hajr killed more than 70 jihadists, provincial officials said.
The violence has allowed extremists such as AQAP and the Islamic State group to extend their influence and launch scores of attacks on security forces.
Last month, IS claimed a wave of suicide bombings targeting Yemeni troops in Mukalla that killed at least 42 people.