We have studied the hydration dependence of the internal protein dynamics of hen egg white lysozyme by naturally abundant ~3C and ~H nuclear magnetic resonance (NMR) relaxation. NMR relaxation times T~, off-resonance Tlp and proton-decoupled on-resonance T~p (only for carbon experiments) were measured in the temperature range from 0 to 50~ The spectral resolution in carbon cross-polarization magic angle spinning spectrum allows to treat methine, methylene and methyl carbons separately, while proton experiments provide only one integral signal from all protons at a time. The relaxation times were quantitatively analyzed by the well-established correlation function formalism and model-free approaeh. The whole set of the data could be adequately described by a model assuming three types of motion having correlation times around 10 -4, 10 -9 and 10 -~2 s. The slowest process originated from correlated eonformational transitions between different energy minima, the intermediate process could be identified as librations within one energy minimum, and the fastest one is a fast rotation of methyl protons around the symmetry axis of methyl groups. A comparison of the dynamic behavior of lysozyme and polylysine obtained from a previous study (A. Krushelnitsky, D. Faizullin, D. Reichert, Biopolymers 73, 1-15, 2004) reveals that in the dry state both biopolymers are rigid on both fast and slow time scales. Upon hydration, lysozyme and polylysine reveal a considerable enhancement of the internal mobility, however, in different ways. The side chains of polylysine are more mobile than those of lysozyme, whereas for the backbone a reversed picture is observed. This difference correlates with structural features of lysozyme and polylysine discussed in detail. Due to the presence of a fast spin diffusion, the analysis of proton relaxation data is a more difficult task. However, our data demonstrate that the correlation functions of motion obtained from carbon and proton experiments are substantially different. We explained this by the fact that these two types of NMR relaxation experiments probe the motion of different intemuclear vectors. The comparison of the proton data with our previous results on proton relaxation times T~ measured over a wide temperature range indicates that at low temperatures lysozyme undergoes structural rearrangements affecting the amplitudes and/or activation energies of motions.