Evdokas was born in 1928 in Pachna, Lemesos province, Cyprus. He founded the National Democratic Party and opposed Archbishop Makarios III in the 1968 presidential elections as a die-hard proponent of Enosis (union of the island with Greece. The campaign was marked by abuse with yogurt and other objects hurled at Evdokas. He received just 3.71% of the vote.
Evdokas has authored 16 books on the subject of psychiatry. He has two sons, both resident in the USA.