The kinetic model for a ternary system is introduced based on the microscopic diffusion form of the phasefield equations for a binary alloy. The equation is solved in the reciprocal space. This model is used to investigate the early precipitation process of Ni75Al10V15by simulating the atomic pictures of the two ordered phases and calculating the order parameters ofγ′(Ni3Al) phase. Simulation results show that theγ′ordered phases precipitate from the disordered matrix by a nonclassical nucleation mechanism, and the nonstoichiometricγ′ordered phase appears first and then transforms into the stoichiometric one. Clusters of V atoms appear at theγ′phase boundaries followed by the formation of the nonstoichiometricθordered phase. The farther the location fromγ′phase boundary is, the lower the order degree ofθphase is. There exist two kinds of DO22ordered domains: a horizontal one and a vertical one, related to their adjacentγ′phase boundaries. The model could describe the atomic ordering and composition clustering simultaneously, and any a prioriassumptionabout the new phase structure and precipitation mechanism etc. is unnecessary.……