Dunlevy was born in Donegal in 1905 and gained his medical education at University College Dublin. After qualifying in 1927, Dunlevy held junior appointments in Dublin, Market Drayton and Sheffield. In 1934, Dunlevy took the DMRE, and then held radiological appointments in Bristol and Droitwich. He came in Manchester in 1939, where he was visiting radiologist to Ancoats Hospital, then consultant radiologist to Withington and Crumpsall Hospitals. In 1948, Dunlevy was appointed consultant radiologist to South Manchester Hospital Group. He died on 24 June 1964.