A study of the biogenic polyamines spermidine and spermine, as well as of the diamines H2N(CH2),NH2 (n = 2-10 and n = 12), was carried out by both inelastic neutron scattering (INS) and Raman spectroscopies, for both their undeuterated and N-deuterated forms. Ab initio density functional theory (DFT) methods were also used, to obtain the calculated vibrational spectra of those molecules. A thorough vibrational analysis was performed, leading to the assignment of the solid-state spectra, both Raman and INS, of the polyamines studied, comprising all their longitudinal acoustic modes (LAM's).