Abstract: The machine comprises a clamping structure including a pair of clamping plates which can rotate about a first axis and can be moved towards one another to clamp on the longitudinally opposite sides a container containing the product to be mixed. The clamping structure is arranged to rotate about a second axis perpendicular to the first axis, in such a manner that the container can be caused to rotate simultaneously about two perpendicular axes. An inner driving shaft controls the clamping movement of the plates, while an outer driving shaft controls the rotational movement of the container about the two perpendicular axes. A single electric motor controls the inner and outer driving shafts by means of respective belt transmissions.