The influence of cocrystallized H2O molecules on the terahertz (THz) spectra and corresponding computational treatment of hydrated molecular crystals was investigated in the study of protonated and deuterium-substituted L-serine-H2O. The THz spectra of both solids have been measured in the range of 10 to 90 cm(-1), with simulations of the crystalline structure and THz vibrational modes performed using solid-state density functional theory. Significant and systematic overestimations of the predicted vibrational frequencies were observed in all calculations. Evidence provided by the comparison of the experimental and calculated vibrational frequencies for both the protonated and deuterated L-serine center dot H20 solids indicates the presence of significant anharmonicity in the observed lattice vibrations. The results suggest that vibrational anharmonicity may play a much larger role in the interpretation of the THz spectra of hydrates in contrast to their corresponding anhydrous forms.