  An analysis of the CP violating asymmetry in $K^\pm \to (3\pi)^\pm$ decays in
the Standard Model and, by means of the mass insertion approximation, in a wide
class of possible supersymmetric extensions, is presented. We find that the
natural order of magnitude for this asymmetry is $\cO(10^{-5})$ in both cases.
Within supersymmetric models effects as large as $\cO(10^{-4})$ are possible,
but only in a restricted range of the relevant parameters.
