A systematic study on lattice dynamics of M n + 1 AlC n (n = 1-3) phases using first-principle calculations is reported, where the Raman-active and infrared-active (IR) modes are emphasized. The highest phonon wavenumber is related to the vibration of C atoms. The 'imaginary wavenumber' in the phonon spectrum of Nb 3 AlC 2 contributes to the composition gap in Nb-Al-C system (Nb 2 AlC and Nb 4 AlC 3 do appear in experiments, but there are no experimental reports on Nb 3 AlC 2 ). The full set of Ramanactive and IR-active modes in the 211, 312, and 413 M n + 1 AX n phases is identified, with the corresponding Raman and IR wavenumbers. The 211, 312, and 413 M n + 1 AX n phases have 4, 6, and 8 IR-active modes, respectively. There is no distinct difference among the wavenumber ranges of IR-active modes for 211, 312, and 413 phases, with the highest wavenumber of 780 cm À1 in Ta 4 AlC 3 . The Raman wavenumbers of M 2 AlC phases all decrease with increasing the d-electron shell number of transition metal M. However, this case is valid only for the Raman-active modes with low wavenumbers of M 3 AlC 2 and M 4 AlC 3 .