A bioreactor (1) having a container (2), a shaft housing (3) for guiding a shaft (5) through a wall (7), a stirrer (6) connected to the shaft (5) in the interior (9) of the container (2), and a drive (4) arranged outside the container (2) and connectable to the shaft (5). The shaft (5) is mounted in the shaft housing (3) via at least one ball bearing (23) and is sealed in relation to the shaft housing (3) by at least one seal (11, 20). The seal (11, 20) is configured as a radial shaft seal (28) having two sealing lips (30, 31) that are arranged one behind the other in the longitudinal direction of the shaft (5) and are able to run on the shaft (5) without lubricant.