We discuss the kinetics of order-order and order-disorder transitions in weakly segregated diblock copolymers. A theory is developed based on the anisotropic fluctuations in the ordered phases. These fluctuations play two crucial roles : first, they determine the stability limit of the initial structure and, second, they are responsible for the emergence of new structures, whether these are the final equilibrium states or transient states during the transition. A linear stability analysis allows us to identify the largest fluctuation modes under both equilibrium and nonequilibrium conditions. By combining the order parameter of the initial structure with the largest fluctuation modes into a simplified multimode model we are able to describe qualitatively the full nonlinear evolution of the system after sudden temperature jumps beyond the spinodal of the initial phase. Our theory successfully explains our earlier results from direct Cahn-Hilliard-type numerical simulations. Our predicted kinetic scenarios are in accord with available experiments.