Abstract: A clothes washing machine is provided with an oscillating washing assembly including a rotating drum capable of being driven at various rotating speeds and provided with a plurality of annular hollow bodies secured to the drum. A plurality of moving masses are capable of freely moving within the hollow bodies. Before at least one spin-extraction phase, the drum is driven to rotate in a continuous manner at a variable, relatively low speed which is lower than the resonance frequency of the oscillating washing assembly, but is adequate to cause the washload in the drum to keep adhering against the inner peripheral surface of the drum. As soon as the moving masses succeed in distributing themselves in such a manner that their center of gravity locates itself in a position that is substantially opposite to the unbalance condition of the washload, the drum is started to rotate at the desired spin-extraction rate.