The time dependence of interdiffusion at the interface between two thin films of deuterated and protonated polystyrene has been investigated by neutron reflectometry. Different time regimes can be resolved. First, a very fast intermixing of chain segments of the originally well-separated molecules over a distance of approximately 3 nm takes place. At intermediate times no significant further movement of the chains across the interface is observed. A third time regime with a larger exponent for the movement of chain segments across the interface is found. It is, however, still considerably slower as compared to the square root of t- behaviour expected at large diffusion times, where the diffusion path is larger than the radius of gyration. Data are analysed with a simple model assuming an error-function-type density profile at the polymer interface, but the general conclusions do not depend on the specific model. Results are discussed in terms of the reptation model of polymer diffusion.