Spreading of aqueous drops on hydrocarbon liquids occurs only when particular surfactants are added to the droplets above a critical concentration. For surfactant solutions of didodecyl ammonium bromide (DDAB) in water spreading over mineral oil, rates of droplet expansion are much slower than those corresponding to pure liquids spreading over immiscible liquid substrates with the same initial spreading coefficients. We present a sorption-kinetic model to explain quantitatively the spreading histories for aqueous DDAB droplets on mineral oil. Due to surfactant transport limitations, spreading occurs only when enough surfactant arrives at the dilating lens surfaces to establish a slightly positive, but near-zero spreading coefficient. We solve the convective diffusion equation for a cylindrical disk-like lens under the integral constraint of a constant surfactant adsorption density corresponding to a near-zero spreading coefficient. All observed spreading behavior is correctly portrayed by the proposed sorption-kinetic model including final equilibrium lens formation and spreading rates that are sensibly independent of drop volume, but are strongly dependent on drop surfactant concentration. Quantitative agreement is found with the experimental spreading data for a surfactant diffusion coefficient of 6 x 10(-12) m(2)/s and an effective adsorption rate constant of 6.5 x 10(-7) m/s. Both values prove physically reasonable. The sorption-kinetic model provides a new mechanism for understanding slow surfactant-driven spreading.