The phenomenon of total external reflection (TER) of quasi-monochromatic X-ray radiation fluxes on a material interface and the effect of waveguide–resonator propagation of these fluxes in nanosize extended slit clearance, as well as a device operating on the basis of this effect—a planar X-ray waveguide–resonator—are briefly described. Experimental data on the formation of an X-ray flux by a composite X-ray waveguide–resonator are presented, and a model describing the decrease in the angular divergence of the formed flux without a decrease in the integral intensity is proposed. The model is based on the conception of partial angular tunneling of the radiation flux in the gap between two consequently mounted and mutually adjusted waveguide–resonators; the tunneling is implemented due to the interaction between interference fields of standing X-ray waves excited by the radiation transported by the slit clearance of these waveguide–resonators. © 2018, Pleiades Publishing, Ltd.