A model for diffusion and phase separation which takes into account relaxation of the atomic diffusion flux to its local equilibrium state is explored. This model is described by a partial differential equation of a hyperbolic type that can be called “a hyperbolic model for spinodal decomposition”. Analysis of the hyperbolic model is given to predict critical parameters of decomposition (such as amplification rate of decomposition, speeds for atomic diffusion, and critical time for instability) in comparison with the outcomes of the Cahn-Hilliard theory. From the analytical treatments it is shown that the hyperbolic model predicts non-linearity in the amplification rate of decomposition, which is governed by the ratio between diffusion length and correlation length.