We study morphological transitions between microphase-separated structures in diblock copolymers. By means of the two-mode approximation, kinetics of order-disorder (ODT) and order-order transitions (OOT) in the weak-segregation. limit are investigated by solving numerically a coupled set of the amplitude equations for the fundamental modes. Breakup and reconnection of domains during the morphological transitions are explored in detail. Furthermore, we identify the metastable or unstable intermediate structures which appear in the process of ODT and OOT. The linear stability analysis is also applied to see the most unstable mode when a lamellar structure is destabilized.