Molecular dynamics computer simulations of an alanine dipeptide molecule in aqueous solutions have been carried out. Three different molecular conformations (alpha, beta, and C-7(ax)) have been considered. Structural and dynamical properties of the hydration water molecules have been calculated separately for solvent molecules surrounding different atoms or atomic groups of such dipeptide, i.e., two carbonyl oxygens, three methyls, and two amide hydrogens. The results for the three conformations have been compared for possible differences. The study includes molecule sites--water radial distribution functions and coordination numbers as well as residence times, hydrogen bonding, and reorientational times of water molecules in the hydration shells. The little differences between the properties of water around the polar and nonpolar atomic groups have been carefully analyzed. The discrepancies between the hydration water properties on the different conformations are not significant.