The mechanical behavior of two Fe-Mn-Si based alloys, with and without Cr-addition respectively, was investigated. For a specific allo), the starting stress (sigma(M)) and strain-hardening exponent (n(j)) for stress-induced fcc(gamma) --> hcp(epsilon) martensitic transformation decrease when the training cycle number increases. while the starting stress (up). the corresponding starting strain (epsilon(p)) and strain-hardening exponent (n(2)) for permanent deformation increase. It is Suggested that the decrease of sigma(M) and n(j) and the increase of epsilon(p) are related to the more favorable Schmid factor being approached during the course of trainings while the increase of sigma(p) and n(2) is originated from the accumulation of permanent deformation occurred in the previous cycles.