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We derive analytical expressions for the relaxation time of disordered binary alloys, which quantify the influence of correlations on the relaxation behavior of the concentration wave amplitudes within a linear kinetic theory. The main characteristic of our model is that it does not limit the effective radius of atomic interaction and correlations in the system. Lattice displacements caused by atomic size mismatch are naturally contained in the formalism. The results are applied to an ordering model system. Using two iterations of the recently developed correlation correction algorithm, we show that only a highly accurate correlation function allows one to predict the most stable modes of the fluctuation spectrum.