[en] The kaon radiative decay K⁺ → π⁺πsup(o)ν and K⁺ → π⁺νν have been considered in the vector meson dominance approach with account for the Wess-Zumino-Witten anomaly. The K⁺ → π⁺πsup(o)ν direct emissian amplitude and K⁺ → π⁺νν decay width are shown to be dominated by chiral anomalies.The contribution to the decay is also made by charged pion polarizability. In the frame of the chiral model different contributions into kaon decay amplitudes have been singled out as well as their branching ratio has been evaluated. The experimental consequence of the theory, in particular, the possibility for the CP violation effects search in K^+- → π^+-πsup(o)ν decays have been discussed