The dynamics of water molecules in the hydration layers of proteins are critical for biological function. Here the molecular dynamics in aqueous solutions of model hydrophilic and amphiphilic dipeptides are studied as a function of concentration using the ultrafast optical Kerr effect (OKE). The OKE is a direct time-domain method which yields both picosecond time scale molecular dynamics and low-frequency (Terahertz) Raman spectra, which contain information on the hydrogen-bonded structure of aqueous solutions. Two distinct concentration regimes are identified, above and below 0.4 M peptide concentration. In the low-concentration regime the tetrahedral water structure is largely preserved but the structural dynamics in water are slowed significantly by interaction with the peptide. The slow down is more marked for the hydrophilic than the amphiphilic peptide. Suppression of water structural dynamics observed is greater than that reported for retardation of the water reorientation in NMR, reflecting the different dynamics probed by these different methods. Above 0.4 M the tetrahedral water structure is more strongly perturbed, a contribution to the THz Raman spectrum from the solvated peptide is observed, and structural dynamics in the solution are markedly slowed. This is assigned to slow relaxation within an H-bonded network of peptide molecules. The strong concentration dependence observed goes some way toward explaining disagreements between different measurements of the dynamics of peptide solvation which have appeared in the literature.