  The loss mechanisms of slow interface waves in the layered resonant media are
examined and illustrated by the examples of (i) surface plasmon polaritons in
an isotropic plasma layer, (ii) magnetoplasmons in magnetised plasma and (iii)
spin waves in ferrimagnetic layers. It is shown that losses of all these
interface waves grow at the same rate of Im(gamma) ~ Re(gamma^3), where gamma
is the wavenumber. These abnormal losses are caused by vortices of the power
flow of the interface waves near their resonance cut-off. The basic properties
of the slow interface waves discussed in the paper are inherent to the waves of
hyperbolic type in the layered resonant media.
