In the first incident, unidentified gunmen fired at two policemen on Topi Road in Swabi district of Khyber-Pakhtunkhwa province.
One policeman was killed instantly while the other was seriously injured.
The injured policeman was taken to Swabi Hospital, where he succumbed to his injuries.
Following the attack, security forces cordoned off the area and conducted a search operation.
In the second incident, suspected militants riding a motorcycle fired at a polio vaccination team in a village in Jamrud region of Khyber tribal region. A member of the team was killed, TV news channels reported.
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Pakistan is one of only three countries where the polio virus is still endemic and efforts to stamp out the crippling disease have been hit by the attacks on health teams.
The country has registered 72 cases of polio this year, compared to 58 in 2012.
India this week announced that travellers from Pakistan and other polio-affected countries would have to furnish evidence of vaccination against polio.