We consider nonequilibrium adsorption to a freshly formed surface. Owing to the initial lack of equilibrium, the common diffusion-control assumption is inconsistent at small times. A uniform small-time asymptotic approximation is constructed for a Langmuir-type system in terms of the small parameter epsilon representing the ratio of the respective kinetic and diffusive time scales of the problem. The diffusion-control approximation becomes valid only when t>>epsilon. The adsorption results are applied to the calculation of the dynamic surface tension.