While the raw material type and the production method of micro- and nanofibrillated celluloses (MNFC) strongly affect the absolute values of the rheological parameters of their aqueous suspensions, the dependence of these parameters on consistency, c, is found to be uniform. The consistency index and yield stress of MNFC suspensions follow generally the scaling laws K ~ c^2.43 and tau_y ~ c^2.26, respectively, and a decent approximation for flow index is n = 0.30*c^-0.43. The variability of reported scaling exponents of these materials is likely mainly due to experimental uncertainties and not so much due to fundamentally different rheology. It is suggested that the reason behind the apparently universal rheological behavior of MNFC suspensions is the strong entanglement of fibrils; the flow dynamics of typical MNFC suspensions is dominated by interactions between fibril flocs and not by interactions between individual fibrils.