The present invention is directed to a process and composition for dyeing hair, the composition containing:(a) greater than 10% by weight, based on the weight of the composition, of at least one fatty acid alkanolamide(b) at least one C6-C36 dicarboxylic acid(c) at least one water soluble base capable of reacting with the at least one C6-C36 dicarboxylic acid (b) to form a soap(d) at least one conditioning polymer (e) at least one oxidation dye and(f) optionally, at least one oxidizing agent, wherein the composition is in cream form.