The paper presents equations to determine concentration changes in time at the outlet of single homogeneous tanks and homogeneous tank cascades. Using these equations, one can specify the required capacity of the facilities that will provide necessary damping of concentration oscillations at their outlets. The additional calculations performed by the author shows that the cascade of homogeneous averaging tanks and cascade of homogeneous retention- -averaging tanks also exhibit similar properties of damping concentration oscillations. For some specific cases of dynamics of concentrations and residence times changes for the substances within the tank, to damp concentration oscillations at the same level, the required capacity of the cascade tank can be smaller than the capacity of a single homogeneous tank. Damping of concentration oscillations by a tank cascade may be better than the attenuation by a single homogeneous tank of the same capacity. The same concentration oscillations damping effect can be, obtained for two different tank cascades, occasionally.