Bioreactor (1) with a fastening device (4, 4', 4'') for the correct orientation of a shaft (3) penetrating a wall (5, 5', 5'') orthogonally to a reactor interior (2), with a shaft-side first connection part (9, 9', 9'') which has a shaped body (14, 14', 14'') with which it is connected by positive locking in a rotationally secure manner to a shaped body receptacle (15, 15', 15'') of a wall-side second connection part (10, 10', 10''), characterized in that the second connection part (10, 10', 10'') is fixedly connected to the wall (5, 5', 5'') or that the second connection part (10'') is part of the wall (5''), and that the shaped body (14, 14', 14'') of the first connection part (9, 9', 9'') and the shaped body receptacle (15, 15', 15'') corresponding to the shaped body (14, 14', 14'') of the second connecting part (10, 10', 10'') are formed asymmetrically in a
transverse plane arranged transversely to the longitudinal axis (16) of the shaft (3).