An overflowing cylinder (OFC) provides a convenient method for studying nonequilibrium liquid interfaces under steady-state conditions. In the presence of surfactants in solution, large accelerations in the surface velocity are observed as a result of Marangoni effects. The surface expansion rate is approximately uniform over the surface of the OFC and falls in the range of 1-10 s(-1). In this paper, a quantitative model is presented for the mass transport to the expanding surface of the OFC. The model is then used to analyze experimental measurements of surface expansion rates and surface excess for solutions of a cationic surfactant, hexadecyltrimethylammonium bromide (CTAB), obtained by laser Doppler scattering and neutron reflection, respectively. The experimental results are in satisfactory agreement with the predictions of diffusion-controlled adsorption close to the critical micelle concentration (cmc). At concentrations well above and well below the cmc, kinetic barriers to adsorption appear to exist. The data at low concentrations are discussed in terms of a model for mass transport through the electrical double layer. At high concentrations, double-layer effects are negligible and steric barriers to adsorption are postulated.