The hydrodynamic model of steady wetting developed by Boender et al. is extended to include the effect of a (nonionic) surfactant in the limiting case of negligible diffusion and low concentrations, confining attention to steady wetting between parallel plates. The approximation that the meniscus inclination becomes equal to the static contact angle at a distance from the solid of the order of a molecular dimension is extended to take account of the local surfactant concentration, making use of Young's law. A second inner boundary condition, provided by a surfactant balance at the contact line, places a restriction on the speed at which the interface is shed, leading to surfactant accumulation and partial or almost total immobilization of the interface which reduces the wetting speed. Under certain conditions, this immobilization is self-stabilizing, leading to hysteresis effects. Both these effects and the reduced wetting speed correspond with results reported in the literature.