  We propose a mechanism for the damping of density oscillations in
multicomponent compact stars. The mechanism is the periodic conversion between
different phases, i.e., the movement of the interface between them, induced by
pressure oscillations in the star. The damping grows nonlinearly with the
amplitude of the oscillation. We study in detail the case of r-modes in a
hybrid star with a sharp interface, and we find that this mechanism is powerful
enough to saturate the r-mode at very low saturation amplitude, of order
$10^{-10}$, and is therefore likely to be the dominant r-mode saturation
mechanism in hybrid stars with a sharp interface.
