While the connection between imaginary frequency instalitaneous normal modes (TNM) and barrier crossing in liquids is well established, nondiffusive modes exist which must be removed in theories of the self-diffusion constant, D. It is shown that in molecular systems rotation is the primary source of such modes. A new type of pure translation (TR) INM is introduced, describing center-of-mass motion. TR densities of states, [rho(TR)(omega)], are obtained at several T for CS2. The TR Im-omega modes vanish at the glass transition and their fraction, f(u)(TR), has a T dependence identical to that of D. Correspondingly, the Re-omega density looses the usual INM linear low-omega dependence and attains conventional omega(2) behavior. It is proposed that the unmodified TR INM have a negligible nondiffusive character and naturally describe translational dynamics in molecular systems. Some general ideas are given for how INM properties, including the importance of nondiffusive modes, vary among different materials. (C) 1997 American Institute of Physics.