We have investigated the ordering dynamics of a triblock copolymer of a polystyrene-block-polyisoprene-block-polystyrene with asymmetric composition from the disordered sphere phase, where spherical microdomains exist but they have only a short-range liquidlike order, to the cylindrical and spherical microdomains with a long-range order. The ordering process was explored in situ by time-resolved small-angle X-ray scattering (SAXS), and the microdomain structures during the ordering process were observed by transmission electron microscopy (TEM) on specimens frozen at particular times in the ordering process. The SAXS observations show that there is an incubation period before the formation of the cylindrical and spherical microdomains with a long-range order. The coexistence of the ordered grains and the disordered spheres was observed in the TEM pictures taken during the ordering of both cylinders and spheres. The coexistence of the ordered grains and disordered spheres together with the existence of the incubation period suggests that this ordering proceeds via a nucleation and growth process. Moreover, it is revealed that the shape of the ordered grains in the matrix of the disordered spheres highly depends on the microdomain structures.