  The dynamics of a tracer molecule near a fluid membrane is investigated, with
particular emphasis given to the interplay between the instantaneous position
of the particle and membrane fluctuations. It is found that hydrodynamic
interactions creates memory effects in the diffusion process. The random motion
of the particle is then shown to cross over from a ``bulk'' to a ``surface''
diffusive mode, in a way that crucially depends on the elastic properties of
the interface.
