The librational motion in the α phase of solid N2 and CO has been studied in the approximation that the centers of mass of the molecules are fixed at the lattice sites (i.e. no translational motion). The potential between two molecules in the crystal was taken to be that derived by Kohin modified slightly to ensure that the molecules are in equilibrium at the measured lattice spacing at T = 0. This potential was expanded in the angle deviations of the molecules from their equilibrium orientations, and the librational frequencies at zero wave vector were calculated in the harmonic approximation. The results were found to be as much as 1.9 times higher than the frequencies measured by Raman scattering. This is attributed mainly to the failure of the harmonic approximation rather than to lack of knowledge of the parameters in the potential. This conclusion is supported by a simple calculation of the root mean square angular deviation of a molecular axis from its equilibrium orientation which for α-N2 is estimated to be 18° at T = 0. Finally, it is emphasized that the anisotropic attractive and repulsive dispersive terms and the quadrupole–quadrupole interaction make comparable contributions to the librational frequencies.