Two children and eight security forces were among the casualties, said Ataullah Khogyani, spokesperson for the Nangarhar provincial government.
It was not clear what caused the explosions.
No group took immediate responsibility. Islamic State emerged in Nangarhar in 2015 on the porous border with Pakistan to become one of Afghanistan’s most dangerous militant groups for its bombing and complex attacks.
Fighting between militant groups, and between the Taliban and Afghan forces has intensified in recent weeks amid recurring peace talks.
This story will be updated accordingly
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