At the regional level he won the 1987 All-Africa Games as well as three gold medals at the African Championships.

He won an Olympic bronze medal in 4 x 400 metres relay in Los Angeles 1984.

He also won the gold medal in the 200 metres at the 1983 Summer Universiade with a personal best of 20.42 seconds; he followed this by finishing 6th in a world class field in the 200 metre final at the 1983 World Championships in Athletics in Helsinki.

Egbunike is currently the head coach of Pasadena City College's track and field team.

Egbunike is good friends with former Kansas City Chiefs' running back Christian Okoye and met him when they were both training for Nigeria's national track and field team.