The incoherent neutron scattering cross section of molecular liquids is evaluated using correlation function descriptions of molecular translations and rotations. The calculation is based on the Gaussian approximation for the intermediate scattering function, and the analysis is specifically directed at the energy region of thermal and cold neutrons. Physical models are used to calculate the translational and rotational effects in the mean-square displacement (width) function, or equivalently, the generalized frequency distribution, and it is assumed that translation-rotation couplings can be ignored. The description of center-of-mass motions properly includes the short-time vibrations as well as the long-time diffusion. Different rotational models are discussed, and a simple expression is suggested which relates the rotational correlation function to the Fourier transform of a near infrared vibrational absorption band. Explicit calculations are carried out for liquid methane, and the results are in quite satisfactory agreement with both thermal- and cold-neutron measurements. The results also indicate that inelastic scattering effects are mostly due to rotational motions. Total cross sections are computed and found to agree with experiment (to within 3%) in the range 1-50 × 10−3 eV.