A Babylonian scholar of the fourth and fifth amoraic generations (fourth century), son of the celebrated ABAYE Naḥmani, and presiding judge in Pumbedita (Yeb. 75b; Ket. 85a), where his father had directed the academy. Some rabbinic chronologists (J. Schorr, "Wa'ad Ḥakamim," 24b; Bacher, "Ag. Pal. Amor." 3:667, note 5) suggest his identity with Bebai II., which, however, is chronologically incorrect (compare Heilprin, "Seder ha Dorot," , s. "Bebai b. Abin"), the latter having been a fellow-pupil of Rab Joseph, whereas Bebai b. Abaye was a contemporary of Naḥman b. Isaac, Kahana III. (Ber. 6b; 'Er. 90a), Pappi, and Huna b. Joshua. As Abaye was a scion of the priestly house of Eli, which was doomed to premature death (1 Samuel 2:33; see R. H. 18a), both Pappi and Huna b. Joshua frequently taunted Bebai with being descended from frail (short-lived) stock, and therefore with uttering frail, untenable arguments ('Er. 25b; compare "Diḳduḳe Soferim" a.; B. M. 109a; B. B. 137b, 151a; compare Jastrow, "Dict." 794a, s. "Mammulaë"). Bebai b. Abaye seems to have led a contemplative life; and legend relates some curious stories about him (Ḥag. 4b; Ber. 6a; Ber. 8b; 'Er. 8a; Shab. 3b, 4a; Ḥul. 43b; Ker. 3b; Zeb. 107a.).