Four explosions in different parts of the city took the lives of two people and injured three others, eyewitnesses told TOLOnews.
Those wounded have been transferred to the hospital in the provincial center.
In the meantime, a gunmen attack in an area near a base of the border forces of the former government resulted in three people killed.
No details have been obtained on the intended target of the attacks.
The head of the information and culture department of Nangarhar province said all those killed and wounded were civilians and no Taliban forces were harmed in the attack.
So far, no group has claimed responsibility for the explosions or attack by gunmen.
Earlier this week, however, Daesh claimed responsibility for previous explosions in Nangarhar.
Daesh also claimed responsibility for the explosions outside Kabul airport in August.
The attacks follow repeated statements by Zabihullah Mujahid, deputy minister for the Ministry of Information and Culture, that Daesh movements in Afghanistan are not at a scale that could pose a security threat.
Mujahid has also said that Taliban forces have the capability to counter Daesh.