  We study specific features of the scattering of gravitational waves on
wormholes and normal matter objects. We derive and solve the GW energy
transport equation and show that the scattered signal lies in the same
frequency spectrum bands as the basic signal. The scattering forms specific
long living tails which always accompany the basic signal and have a universal
form. The scattering on normal matter objects forms tails which have always the
retarding character, while wormholes lead to advanced tails as well. In
addition, wormholes may produce considerably stronger effect, when the total
energy in tails exceeds the energy of the incident wave by the factor up to
$10^{3}$ . In both cases the retarding tails have a long living character when
the mean amplitude behaves with time as $h\sim 1/\sqrt{t+R/c}$. For a single GW
event the echo tails give only a tiny contribution to the mean amplitude.
However such tails accumulate with events and may be observed by their
contribution to the noise produced by the stochastic GW background.
