The diffusion coefficient in aqueous solution of lysozyme has been measured by means of the optical beating spectroscopy, at different concentrations and scattering angles. It has been found that the decay of the fluctuation of the concentration cannot be represented by a single exponential law. There is a long tail associated with some slow decaying quantity. In addition, both the short- and the long-time behaviour turns out to be angle and concentration dependent, indicating the existence of some sort of structure. The commonly accepted literature value for the diffusion coefficient is recovered only in the limit of large scattering vectors. The above-mentioned results are also discussed in the frame of other experimental results obtained for the same system.