The aim of this theoretical investigation is the description of the multicomponent mass transfer process in the Nano- Composites (NC)—novel materials with the bi-functional matrix. The new theoretical NC Model is assigned for the modern theoretical investigations of the multicomponent mass transfer kinetics in the bi-functional NC materials. This NC Model for the multicomponent mass transfer in the bi-functional NC matrix includes into the consideration the proposed key conception—two co-existing routes: I—chemical reactions onto the active NC centers-sites, and II—diffusion mass transfer inside the bi-functional NC matrix. All the results are presented in the terms of the additional key concept: propagating multicomponent concentration waves (W⁺) in the NC matrix. The used W⁺ concept for the description of the multicomponent NC mass transfer kinetics give the clear interpretation of the computerized results. The mass transfer process in the NC matrix has been described theoretically by computerized simulation. The results of the calculations are new and illustrated by author’s animations showing visually the propagation of the multicomponent concentration waves (W) inside the various NC matrixes: r-beads, cylindrical ro-fibers, or planar L-membranes. Two variants of modeling for mass transfer diffusion kinetics in the bi-functional NC matrixes with one (Variant 1), or two (Variant 2) dissociation-association reactions at the active nano-sites (R⁰) are considered theoretically.