The present invention is directed to a process and composition for dyeing hair, the composition containing: (a) greater than about 10% by weight, based on the weight of the composition, of at least one fatty acid alkanolamide; (b) at least one C.sub.6-C.sub.36 dicarboxylic acid; (c) at least one water soluble base capable of reacting with (b) to form a soap; (d) at least one conditioning polymer; (e) at least one oxidation dye; and (f) at least one oxidizing agent, wherein the composition is in cream form.