A cosmetic or dermatological composition, comprising an oil-in-water emulsion comprising oily globules which are each coated with a lamellar liquid crystal coating and are dispersed in an aqueous phase, each oil globule comprising at least one lipophilic compound which is cosmetically or dermatologically active and is individually coated with a monolamellar or oligolamellar layer of a mixture of at least one lipophilic surface active agent, at least one hydrophilic surface-active agent, and at least one fatty acid, said coated oil globules having a mean diameter of less than 500 nanometers, and said aqueous phase comprising a basic agent in the dissolved state, wherein said lipophilic surface-active agent, said hydrophilic surface-active agent, and said fatty acid are present in a combined amount of between 2 and 6% by weight based on the total weight of said composition.