Abstract: A process for permanently deforming keratin fibers and compositions suitable for use in this process are provided. The process includes treating keratin fibers, before and/or after mechanically deforming the keratin fibers, with an aqueous reducing composition containing a keratin reducing substance, rinsing the keratin fibers with a rinse after contact with the reducing composition, and applying to the keratin fibers an aqueous fixing composition containing an oxidizing agent, where at least one of the reducing composition, the fixing composition, or the rinse is in the form of a two-phase or multiphase system. The two phase or multiphase system contains at least one oil component and/or at least one alcohol having limited miscibility with water and is capable of being converted at least temporarily with mechanical agitation into a homogeneous system for application to hair.