The classical centrifugal-sudden approximation (cCSA) in molecular collision dynamics is studied. Following the traditional quantal approach, the problem is first formulated in the body-fixed (BF) coordinate system exactly. Attempts to deduce the cCSA from the BF Hamiltonian, however, fail to provide proper directional information for the relative motion. Instead, the cCSA can be derived from the uncoupled angular momentum representation in the space-fixed coordinate system, and directional information can then be obtained. The cCSA is applied to the study of transport and relaxation cross-sections of the He-N2and Ar-N2systems. For both systems the dynamical error is investigated by comparing the cCSA results with exact classical trajectory results, while for the He-N2system the quantization error is obtained by comparing the cCSA and quantal centrifugal-sudden approximation results. The cCSA is found to be accurate for the viscosity and diffusion cross-sections. Encouraging results were found for the relaxation cross-sections for depolarized Rayleigh light scattering, the viscomagnetic effect and the field effect on the thermal conductivity. When comparisons are possible, the quantization error is usually found to be larger than the dynamical error.