Molecular dynamics (MD) of stationary chemical kinetics is used to simulate oscillating chemical reactions in a system of N classical mechanical particles with Lotka-Volterra kinetics. The MD includes oscillations in a (closed) system with conserved energy and time reversible dynamics as well as oscillating chemical reactions in an open and driven non-equilibrium system, and with and without a competing phase separation of the different components in the reactions. The approach allows a detailed investigation of the kinetics and demonstrates on a molecular level, the phenomenon oscillating reactions for various chemical and reaction kinetics details. When phase separation takes place during the oscillations the kinetics is no longer simple diffusion driven. (C) 1997 American Institute of Physics.