  We study the scattering of the $\varphi^8$ kinks off each other, namely, we
consider those $\varphi^8$ kinks that have power-law asymptotics. The slow
power-law fall-off leads to a long-range interaction between the kink and the
antikink. We investigate how the scattering scenarios depend on the initial
velocities of the colliding kinks. In particular, we observe the `escape
windows' -- the escape of the kinks after two or more collisions, explained by
the resonant energy exchange between the translational and vibrational modes.
In order to elucidate this phenomenon, we also analyze the excitation spectra
of a solitary kink and of a composite kink+antikink configuration.
