The kinetics of the microphase separation transition in a diblock copolymer of polystyrene/polyisoprene was studied with time-resolved small-angle X-ray scattering. Using synchrotron radiation it was possible to determine the structure factor in time intervals of 10 s. The relaxation of the structure factor after temperature jumps within the disordered regime was found to be wave vector dependent in accordance with Cahn-Hilliard theory. For quenches from the disordered into the ordered state an additional, slow process was found which consists mainly of a decrease in the width of the first-order reflection. It is interpreted as the perfectioning of the lamellar order. Whereas the corresponding relaxation time had been found to decrease strongly with supercooling for shallow quenches, it is found to increase again for deeper quenches.