Eulogius (Greek Eulogios) was a Syrian Greek-tradition Catholic monk who became Patriarch of Alexandria in 581. He governed the Chalcedonian-Catholic ('Melkite,' or 'King's-faction') minority Christian community of Egypt for 27 years through the difficult post-Justinianic period when the substantial Coptic-Miaphysite majority population of Egypt was substantially out of communion with the Roman-Constantinopolitan Chalcedonian tradition.
Eulogius was a personal friend and correspondent of Pope Gregory the Great. The substantial surviving Gregory–Eulogius correspondence (preserved in Gregory's Registrum Epistolarum) is one of the foundational late-antique Catholic theological-pastoral correspondences and includes substantial doctrinal and pastoral exchange. Gregory's letters to Eulogius are foundational documents of the late-antique Roman-Alexandrian Catholic communion.
Eulogius wrote extensively against the various Monophysite-Miaphysite Christological positions of his Alexandrian context — particularly against the Severan, Theodosian, and Gaianite Monophysite factions. His substantial Greek theological corpus (much of which is now lost, surviving only in fragments preserved by Photius and other later Byzantine sources) was a foundational defence of Chalcedonian Christological orthodoxy. He died at Alexandria on February 13, 608.