Disclosed herein is a composition in the form of an emulsion for shaping or altering the shape of hair such as by straightening hair wherein the composition contains a reducing agent a neutralizing agent at least two fatty substances a nonionic surfactant selected from alkoxylated fatty alcohols and alkyl(ether)phosphates optionally a quaternary ammonium compound and water wherein the pH of the composition ranges from about 2 to less than about 7. Also disclosed is a process for shaping or altering the shape of hair.