We report molecular dynamics (MD) simulations of aqueous solutions of glucose and maltose. For each sugar, two concentrations were studied. The static and frequency-dependent dielectric properties of the solutions were calculated from MD trajectories of at least 5 ns length and compared to those of pure water. The contributions from the solute, the solvent, and the solute-solvent cross term were analyzed. In addition, for the more dilute glucose and maltose solutions a Voronoi analysis was carried out to distinguish between contributions from the first water shell and from unbound bulk water. The results of the glucose simulations were compared to available experimental data. While the static dielectric constant of the four solutions was found to be very similar to that of pure water, a number of differences could be discerned in the dielectric spectra. These findings for the overall frequency-dependent dielectric susceptibilities were rationalized by a dielectric component analysis. The importance of contributions from cross terms and from the solute depended on solute type (glucose or maltose) and concentration. In particular, we observed a linear correlation between the contribution of the solute-solvent cross term and the total number of hydroxyl groups of the solute (i.e., the number of solute molecules times the number of hydroxyl groups in a glucose or maltose molecule, respectively). The dielectric properties of water in the solutions could be rationalized as the superposition of two contributions, one originating from the bulklike free waters, the other from the waters in the first hydration shell of the saccharides.