Hunger was from 1956 to 1962 director of the papyrus collection of the Austrian National Library, 1962-1985 university professor in Vienna and from 1973 to 1982 President of the Austrian Academy of Sciences. He founded the Vienna School of Byzantine Studies and was the first Chair of Byzantine Studies at the University of Vienna.
On October 10, 1980 hunger was elected corresponding member of the Philological- historical class of the Saxon Academy of Sciences.
Hunger was buried at Vienna's Central Cemetery.
- Grand Commander of the Order of the Phoenix of the Hellenic Republic
- Great Cross of Merit with Star of the Order of Merit of the Federal Republic of Germany
- 1979: Prize of the City of Vienna for the Humanities
- 1981: Austrian Decoration for Science and Art
- Grand Gold Decoration for Services to the Republic of Austria
- Grand Gold Decoration for Services to the City of Vienna
- Greek paleography, 1954
- Byzantine spirit world, 1958
- Dictionary of Greek and Roman mythology, 1959 ( 8th edition 1988)
- Ancient and medieval book and type beings. Tradition history of ancient literature, 1961
- Empire of the new center. The Christian spirit of Byzantine Culture, 1965
- Catalogue of the Greek manuscripts in the Austrian National Library, ( 6 volumes, 1961-1995 )
- Byzantine Basic Research, 1973
- The highly profane language literature of the Byzantines, 2 volumes, 1978
- Epidosis, 1989 ( collected works )
- Reading and writing in Byzantium, 1989
- Prochoros Kydones, 1990
- The thinking at the reins of language, 1999