  The calculations of isotopic amplitudes and their results for the direct
$CP$--violating charge asymmetry in $K^\pm \to 3\pi$ decays within the
nonlinear and linear ($\sigma$--model) chiral Lagrangian approach are compared
with each other. It is shown, that the latter, taking into account intermediate
scalar resonances, does not reproduce the $p^4$--corrections of the nonlinear
approach introduced by Gasser and Leutwyler, being saturated mainly by vector
resonance exchange. The resulting differences concerning the $CP$ violation
effect are traced in some detail.

High Energy Physics - Phenomenology