Molecular dynamics simulations of the hen egg-white lysozyme-Fab D1.3 complex were performed, starting from the X-ray crystallographic coordinates obtained by Fischmann et al. [J. Biol. Chem. 1991, 266, 12915-12920], and including counterions and explicit random water molecules. Both the crystal state and the complex in solution were studied, the former as the asymmetric unit cell in interaction with all its neighbors, and the latter with a new model (the "egg") consisting of a truncated ellipsoid containing the complex and solvent molecules, a first shell with additional solvent, and two further shells with virtual solvent molecules derived from those of the first shell by a geometrical correspondence. The hydration structure of the complex is analyzed from the data obtained after equilibration and fluctuation dynamics of these two systems. The water density around the protein is found to increase, up to a maximum of 1.5 for the complex in solution, so that the integrated density largely exceeds unity. Therefore additional water molecules were steadily included into the "egg" model. In the crystal cell model an average density of unity was conserved. Detailed analyses are given of the pair correlation functions, coordination numbers, local water density, and orientations of water molecules. Two hydration shells are observed around the complex in solution, the inner one with molecular orientations very dependent on the local character of the protein surface (either nonpolar, or positively or negatively charged), whereas the second shell which extends continuously toward the bulk is essentially homogeneous, apart from slight residual orientational preferences of the dipole moments in the first few A of this shell when the closest protein atom is positively or negatively charged. Comparisons of the root-mean-square fluctuations of the protein backbone atoms from the simulations of the complex in the crystal state and in solution with experimental B factors from the X-ray crystallographers show the importance of a correct description of the water density around the protein. It is argued that the absence in the crystal cell of a bulklike aqueous phase may lead to a higher mobility of the protein chains in the crystal than in solution.