Year 368 (CCCLXVIII) was a leap year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Augustus and Valens (or, less frequently, year 1121 Ab urbe condita). The denomination 368 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

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• Eustochium, Christian Desert Mother and saint (approximate date)
• Juqu Mengxun, Chinese prince of the Northern Liang (d. 433)
• Philostorgius, Anomoean church historian and writer (d. 439)

• July 7 – Maternien, Christian bishop and saint