[en] The problem of scattering of the background radiation on relic cosmological wormholes is considered. It is shown that static wormholes do not perturb the spectrum at all. The presence of peculiar velocities of wormholes results in a distortion of the CMB spectrum which is analogous to the kinematic Sunyaev-Zel’dovich effect. In the first order in $v/c$ the distortion of CMB cannot be separated from the Compton scattering on electrons. In next orders the scattering on wormholes exhibits some difference from the Compton scattering. High-energy cosmic-ray particles spectrum does not change the form by KSZ, but undergoes a common Doppler shift. Such features may give a new tool to detect the presence of relic wormholes in our Universe.