Some surfactants form, in solution, long wormlike micelles. We study, theoretically, a binary solution of such surfactants which form micelles separately. For a wide range of intermicelle interactions, the surfactants are found to demix into two phases, one rich in each of the surfactants. We also study mixtures of wormlike micelles with small colloidal particles and again find that for a wide range of interactions there is demixing. The wormlike micelles behave in an analogous way to polymers; however, the length of micelles differs between phases which are surfactant rich and surfactant poor.