Deuterium (H-2) magic-angle spinning (MAS) nuclear magnetic resonance is applied to monitor the dynamics of the exchanging labile deuterons of polycrystalline L-histidine hydrochloride monohydrate-d(7) and -oxalic acid dihydrate-d(6). Direct experimental evidence of fast dynamics is obtained from T-1Z and T-1Q measurements. Further motional information is extracted from two-dimensional single-quantum (SQ) and double-quantum (DQ) MAS spectra. Differences between the SQ and DQ linewidths clearly indicate the presence of motions on intermediate timescales for the carboxylic moiety and the D2O in -oxalic acid dihydrate, and for the amine group and the D2O in L-histidine hydrochloride monohydrate. Comparison of the relaxation rate constants of Zeeman and quadrupolar order with the relaxation rate constants of the DQ coherences suggests the co-existence of fast and slow motional processes.