Broad-band dielectric spectroscopy (10(-2)-10(6) Hz) was employed to investigate molecular dynamics in polyisoprene-polystyrene (PI-b-PS) diblock copolymers with different contents of PI varying from 27.9 to 50.4 wt % and having an identical molecular weight of the PS blocks (2830). The diblock copolymers studied were considered to be thermodynamically homogeneous concerning DSC measurements and having a value of chiN from 5.5 to 8.9 at 25-degrees-C, where chi is the segment-segment interaction parameter and N the number of statistical segments per chain. Two relaxation processes are observed which sense the molecular dynamics of the PI chain in the diblock copolymer on two different length and time scales: The segmental relaxation is a local process corresponding to the primary relaxation of the PI chain in the PI-rich regions of the thermodynamically homogeneous phase. In contrast, the normal-mode relaxation is assumed to be mainly controlled by an effective friction coefficient reflecting the properties of both block components. The normal-model relaxation in its temperature dependence and in its distribution of relaxation times provides evidence for the coupling to composition fluctuations. Furthermore, there is a hint that the freezing-in of PS segmental fluctuations affects the normal-mode dynamics of the PI blocks. Our results are compared to similar investigations by Yao et al.13 on PI-b-PS under conditions of microphase separation. The findings are consistent with the fluctuation picture recently developed by Fredrickson et al. for diblock copolymers near the microphase-separation transition.