A generalized theory for the correlation between the vibration and rotation of partially oriented molecules is developed, retaining the next terms beyond the leading ones in the Taylor series describing the functional dependencies of the internal and external potential energies of the molecules on their normal coordinates. This generalization is shown to be necessary for the cases where the orienting force is very weak due to cancellation of the forces acting on the different parts of the molecule. The theory is used together with the model of bond additivity of the anisotropic forces to reanalyse the dipolar couplings obtained from the N.M.R. spectra of methane and its deuterated analogues dissolved in liquid crystals. The results of the analysis point to the conclusion that the interaction of the methane molecule with its surroundings is dominated by the van der Waals forces acting on its atoms. The resulting information on this external force field provides qualitatively correct predictions about the order parameter of the hydrogen molecule, assuming that the H atoms in H2and CH4experience the same force field. The results also give support to the hypothesis that the orientation-dependent perturbations of the internal state of the molecule are generally dominated by the bond-bending deformations.