There is a variety of experimental evidence for lamellar-to-lamellar phase transitions in aqueous solutions of single- and two-component surfactant systems. We develop here the statistical thermodynamics of alternative scenarios for lamellar-lamellar coexistence. In one case the transition involves phase separation driven by demixing of the two amphiphiles within each bilayer; a purely repulsive interaction between bilayers is sufficient, because of its dependence on bilayer composition. In the complementary case, a condensation-type phase change is involved, caused by the competition between attractive and repulsive interactions; the primary order parameter for this transition is the overall surfactant concentration.