In this paper we study the influence of internal fluctuations on a simple, but realistic model of a chemical system exhibiting oscillatory behavior. The results of molecular dynamics and simulations of the master equation are presented. The period of oscillations and the dynamics of the system obtained in these simulations are in agreement with phenomenology. Two types of fluctuations seem to appear in the simulations : short time scale fluctuations related to stochasticity of elementary reactions and long time scale fluctuations which correspond to random motion of trajectories in the phase space.