Droplets of alkanes on aqueous solutions of the cationic surfactants C(n)TAB (CH3(CH2)(n-1)N+(CH3)(3)Br-) exhibit a first-order wetting transition as the concentration of the surfactant is increased. A theoretical model is presented in which the surface free energy is broken down into a long-range dispersion interaction and a short-range interaction described by a 2D lattice gas, taking into account the interaction between oil and surfactant molecules. The model provides quantitative agreement with the observed wetting transitions and the variation in composition of the wetting film with bulk surfactant concentration. The behavior of oil drops on large reservoirs of dilute surfactant is discussed.