According to the theory of the rate process of diffusion of atoms in lattice, the kinetics of long-range ordering and short-range ordering under the condition of zero long-range order in the nearest neighbour approximation has been investigated. The results obtained agree qualitatively with and quantitatively similar to the conclusions derived from the past experiments and calculations. The results obtained from the calculations of the kinetics of long-range ordering show that the process of ordering requires an induction period, the transformation curves have the form of C-curves and the degree of longe-range order depends upon time in the form of exp {-αt2} -approximately. The equilibrium values of the degree of long-range order obtained are very similar to those of the past workers. The results obtained from the calculations of the kinetics of short-range ordering in the condition of zero long-range order depends upon time in the form of exp {-βt} approximately, and the rate of ordering is so quick, that even with the fastest quenching a certain degree of short-range order exists in the specimen. The equilibrium values of the degree of short-range order also agree with the results obtained in the past.