The dynamic lattice liquid model was implemented as a simulation algorithm for simple liquids. This model works correctly for the density factor rho=1 and becomes a base for a parallel algorithm. Such an algorithm takes into account coincidences of elementary molecular motion attempts resulting in local cooperative structural transformations. In this paper general conditions for simulating simple liquids on various lattices are presented. Interdiffusion coefficients were directly monitored as changes of composition profiles with time for both athermal and interacting binary (AB) mixtures. In the athermal case, the coefficients of self-diffusion and interdiffusion are equal. For interacting binary mixtures the interdiffusion exhibits a thermally activated character. (C) 2003 American Institute of Physics.