The dielectric properties of lysozyme aqueous solutions have been investigated over a wide frequency range, from 1 MHz to 50 GHz, where different polarization mechanisms, at a molecular level, manifest. The dielectric relaxation spectra show a multimodal structure, reflecting the complexity of the protein water interactions, made even more intricate with the increase of the protein concentration. The deconvolution of the spectra into their different components is not unambiguous and is generally a delicate process which requires caution. We have analyzed the whole relaxation region, on the basis of the sum of simple Debye-type relaxation functions, considering three main contributions. Particular attention has been payed to the delta-dispersion, intermediate between the beta-dispersion (rotational dynamics of the protein) and the gamma-dispersion (orientational polarization of the water molecules). This intermediate contribution to the dielectric spectrum is attributed to the orientational polarization of water molecules in the immediate vicinity of the protein surface (hydration water). Our measurements clearly demonstrate that, at least at high protein concentrations, the delta-dispersion has a bimodal structure associated with two kinds of hydration water, i.e., tightly bound and loosely bound hydration water. In the concentration range investigated, the existence of a three-modal delta-dispersion, as recently suggested, is not supported, on the basis of statistical tests, by the analysis of the dielectric relaxations we have performed and a bimodal dispersion is accurate enough to describe the experimental data. The amount of the hydration water has been evaluated both from the dielectric parameters associated with the delta-dispersion and from the decrement of the loss peak of the gamma-dispersion. The relative weight of tightly bound and loosely bound hydration water is briefly discussed.