We investigate the development of mesophase order in compositionally asymmetric (13 wt % styrene) polystyrene-polyisoprene (SI) diblock and SIS triblock copolymers. The equilibrium ordered morphology of these polymers is a body-centered-cubic (bcc) lattice of spherical S microdomains. The ordering kinetics are measured by quenching the material from above the order-disorder transition temperature (T-ODT) to a temperature where the ordered phase is stable and following the structure development by time-resolved small-angle X-ray scattering and dynamic oscillatory rheological measurements. The kinetics are significantly slower than those observed for nearly symmetric polymers of similar T-ODT, resulting in a wider range of experimentally accessible quench depths. The temporal evolution of the storage modulus G’ measured at constant frequency displays a two-step increase after a quench from above the ODT, for sufficiently low temperatures and/or high molecular weights. The long-time step corresponds to the development of a bce lattice of spherical microdomains, while the first step results from the finite time required for large-amplitude composition fluctuations to develop fully.