A computer simulation study on dynamics for the precipitation of δ’(Al_3Li) ordered particles from a disor- dered matrix (α) in binary Al-Li alloys is performed using the microscopic Langevin equation. A unique precipitation mechanism is found near the ordering spinodal line. Different from the classical nucleation mechanism in the me- tastable region and the congruent ordering followed by spinodal decomposition in the instable region, a nonstoichi- ometric single ordered phase with composition fluctuations is formed by non-classical nucleation, and this ordered phase decomposes spinodally. It can be concluded that the precipitation dynamics of δ’ phase from metastability to instability is gradual, and no sharp transition occurs near the mean-field spinodal line as the mean-field theory pre- dicts. A computer simulation study on dynamics for the precipitation of δ ’(Al_3Li) ordered particles from a disor- dered matrix (α) in binary Al-Li alloys is performed using the microscopic Langevin equation. A unique precipitation mechanism is found near the ordering spinodal line. Different from the classical nucleation mechanism in the meastable region and the congruent ordering followed by spinodal decomposition in the instable region, a nonstoichi- ometric single ordered phase with composition fluctuations is formed by non-classical nucleation, and this ordered phase decomposes spinodally. It can be concluded that the precipitation dynamics of δ ’phase from metastability to instability is gradual, and no sharp transition occurs near the mean-field spinodal line as the mean-field theory pre- dicts.