Sublimation of simple aliphatic amino acids (Ala, Aib, Val, Nva, and Leu) at 230 - 250 degrees Celsius under reduced pressure in the presence of silica as a catalyst yields cyclic dipeptides (or piperazine-2,5-diones) as major products. In addition, two types of unusual products have been detected. To determine their structures, we utilized a coupled GC/FTIR/MS technique which enables gas- chromatographic separation along with on-line characterization by FTIR and mass spectra of the products. Based on the spectral data obtained, we suggested the condensation products to be substituted bicyclic and tricyclic amidines, hexahydroimidazo[1,2-a]pyrazine- 3,6-diones and hexahydroimidazo[1,2-a]imidazo-[1,2- d]pyrazine-3,8-diones. To verify this supposition we simulated the IR spectra using the PM3 semi-empirical method. The calculated spectra appeared to be in very good agreement with the experimental ones, reflecting adequately general features of the latter and confirming the proposed amidine structure of the condensation products.