IR spectra of bicyclic and tricyclic amidine derivatives of alanine (2,5,8-trimethylhexahydroimidazo[1,2-a]pyrazine-3,6-dione, 2,5,8-trimethyltetrahydroimidazo[1,2-a]pyrazine-3,6-dione and 2,5,7,10-tetramethylhexahydroimidazo[1,2-a]imidazo[1,2-d]pyrazine-3,8-dione) were computed by the HF, B3LYP, B3P86 and B3PW91 methods in conjunction with the 6-31G(d) basis set. The IR spectra calculated are in a good agreement with the observed FTIR spectra. The correlation between the calculated and experimental vibration frequencies is characterized by the coefficients of 0.9997 for all three DFT methods; for HF it is about 0.9992. The calculated absolute band intensities satisfactory match the observed relative intensities. Optimal uniform scaling factors calculated for this series of compounds are 0.8967, 0.9598, 0.9544 and 0.9555 for HF, B3LYP, B3P86 and B3PW91, respectively. Taking into account small variations of the scaling factors for the derivatives of different amino acids, for future IR spectral predictions for unknown compounds of this class, one can recommend scaling factors of 0.897, 0.959, 0.954 and 0.955 for HF, B3LYP, B3P86 and B3PW91, respectively.