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The kinetic model for a ternary system is introduced based on the microscopic diffusion form of the phase-field equations for a binary alloy. The equation is solved in the reciprocal space. This model is used to investigate the early precipitation process of Ni75-Al10V15 by simulating the atomic pictures of the two ordered phases and calculating the order parameters of γ′(Ni3Al) phase. Simulation results show that the γ′ ordered phases precipitate from the disordered matrix by a non-classical nucleation mechanism, and the nonstoichiometric γ′ ordered phase appears first and then transforms into the stoichiometric one. Clusters of V atoms appear at the γ′ phase boundaries followed by the formation of the nonstoichiometric θ ordered phase. The farther the location from γ′ phase boundary is, the lower the order degree of θ phase is. There exist two kinds of DO22 ordered domains: a horizontal one and a vertical one, related to their adjacent γ′ phase boundaries. The model could describe the atomic ordering and composition clustering simultaneously, and any a priori assumption about the new phase structure and precipitation mechanism etc. is unnecessary.