We investigate the decay of initial vibrational correlations in a dilute gas mixture of diatomic molecules and structureless particles. We use the techniques of Davis and Oppenheim to derive an equation for vibrational relaxation which is suitable for correlated systems. We then use the Landau-Teller transition probabilities and solve for the one-and two-molecule distribution functions and the two-molecule correlation functions. We find that the correlations decay faster than the distribution functions, which agrees with the results of Oppenheim, Shuler,et al. for other systems.