We study the low energy pion-hyperon interaction considering effective nonl
inear chiral invariant Lagrangians including pions, rho mesons, sigma meson
s, hyperons, and corresponding resonances. Then we calculate the S- and P-w
ave phase shifts, total cross sections, angular distributions, and polariza
tions for the momentum in the center-of-mass frame up to k = 400 MeV. With
these results we discuss the CP violation in the Xi --> Lambda pi and Omega
--> Xi pi weak decays.