Analysis of literature data on the flow of polymeric and oligomeric compositions as well as on systems of low viscous dispersion media containing a high-disperse filler (carbon black, silica, high-disperse chalk) has been carried out. As the basic idea, a proposal is made that their viscosity anomaly is due not to the matrix viscosity anomaly, but to the gradual breakdown of the filler structural skeleton with increasing shear stress z and shear rate ~. The viscosity anomaly of those compositions is determined by the zeroshear but not by the apparent matrix viscosity. A general relationship has been found to describe the flow of such systems depending on the zero-shear matrix viscosity values, r/o, their yield stress, z x, and filler volume concentration ~0: r = ry + K~0//~J) ~, where K = 4.9 and n = 0.69 are constants.