The use of generalized Langevin equations in the study of transport processes in simple classical liquids is extended by the derivation of the second such equation in the hierarchy of coupled phase space transport equations. The method introduced is related to the Mori continued fraction representation but poses different points of view for analysis. A truncation procedure is proposed which closes the hierarchy and permits in principle a more accurate description of the first level damping matrix than heretofore available. The theory is applied to the case of self-diffusion for which purpose a simplification of the second generalized Langevin equation is presented, along with a perturbation solution representation of the velocity autocorrelation function. The results obtained are good but still deviate from the observed velocity autocorrelation function.