  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 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.
