Solidp-C6H4(CH3)2andp-C6H4(CD3)2have been studied over a temperature range from 10 K up to the melting point of ∼ 287 K by Raman- and Incoherent Inelastic Neutron-Scattering(IINS). The methyl torsion frequencies deduced from the Raman- and IINS-spectra are different because of the strong coupling of these modes with phonons and their dispersion in the Brillouin zone. A decrease in frequencies and a strong broadening, especially of the high frequency phonons where methyl torsions are predominant, have been observed in Raman- and IINS-spectra with increasing temperature. A lattice dynamics model based on the atom-atom potential set IVa of parameters given by Williams can, after some small modifications, satisfactorily explain the dynamics of ap-xylene crystal. Modified potential parameters better reproduce the experimental data and allow one to study the coupling of the internal methyl rotation with the lattice modes in more detail.