A bioreactor has a reactor bag (12) with a predominantly flexible bag wall (121) that has a rigid bearing area. A stirrer arrangement (14) is in the bearing area and includes rigid profile ring (16) made of a non-magnetic material and fixed in the bearing area. The stirrer arrangement (14) also includes a shaftless stirrer (18) rotatably engaged with the profile ring (16) and having parts that are permanently magnetic. An electric coil arrangement (20) is outside the reactor bag (12) and can produce a rotating magnetic field that interacts with the permanent-magnetic areas of the stirrer (18) to produce a torque that rotates the stirrer (18) and circulates the contents of the bag (12).