Coherent two-phase microstructures consisting of ordered precipitate and disordered matrix phases sometimes exhibit a phase-separation, which brings the split and/or the decelerated coarsening of precipitates. When the coherent two-phase microstructure of A1+L12 (+’) in Ni-base alloys are aged inside the two-phase region of A1+L12 , the L12 precipitate sometimes exhibit a phase-separation and A1 phase newly appears and grows in each L12 precipitate. Phase-separations of the same type to the above also take place due to ageing of coherent two-phase microstructures of A2+D03 and A2+B2 in Fe-base alloys: D03 and B2 precipitates sometimes exhibit phase-separations and A2 phase newly appears and grows in both precipitates. These types of phase-separation take place under the influence of chemical free energy. In the course of further ageing, the new disordered phases of A1 and A2 change their morphology in various ways depending on the elastic constraint: i.e. the morphology of new A1 or A2 phase is influenced by the elastic energies and the surface energy.