This contribution deals with identifiability and local Lipschitz stability for the identfying of cracks with non linear impedances. Identifiability is proven for cracks of same main direction, and impedances spanning the widest possible class making the forward problem well posed, provided the current flux generates singularities. This assumption, which is shown not to be really restrictive, is also needed to prove local Lipschitz stabily, with respect to both longitudinal and transverse virtual moves. Some numerical results will also be presented.