Depolarized light scattering has been applied to study the anisotropy fluctuations in a series of polystyrene/polyisoprene diblock copolymers. This method is selective for the dynamics of the polystyrene block. The molecular weights of the block copolymers (10500-20800) were chosen such that the microphase separation transition (MST) occurs at temperatures which are experimentally accessible with photon correlation spectroscopy. Small-angle X-ray scattering (SAXS) was used to identify the disordered regime, the fluctuation-controlled transition regime, and the ordered state. The relaxation time spectrum in the disordered state is similar to that of bulk polystyrene. Concentration fluctuations increasingly broaden the spectrum and lead to a bimodal shape. Close to the MST the spectrum becomes dominated by a slow, nearly single exponential contribution. Comparison with the SAXS results suggests that this splitting of the relaxation time spectrum can be related to chain stretching.