[en] We report the results of experimental and theoretical studies of the post-filamentation stage of nonlinear propagation of high-power pulsed radiation from a Ti : sapphire laser in air. We have for the first time obtained the experimental dependences of the angular divergence of specific spatially localised high-intensity light structures that are observed in the beam after its multiple filamentation (post-filamentation of channels) when varying the initial focusing of laser radiation and its energy. It is found that the angular divergence of the post-filamentation channels decreases with increasing pulse energy and reducing beam numerical aperture. The experimental dependences are qualitatively interpreted based on the diffraction model of the Bessel – Gaussian beam. (paper)