Dielectric measurements were carried out on homogeneous (not microphase-separated) samples of butadiene (B)-isoprene (I) block copolymers of the BI diblock and BIB triblock types in bulk and in toluene solution. The I block has the component of the dipole moment aligned in the same direction parallel to the chain contour, but the B block does not. We thus were able to investigate dynamics of the I subchains through observation of the dielectric normal-mode process of the I blocks. The nominal relaxation times tau-n of the block copolymers were determined as the inverse of loss maximum frequencies. They strongly depended on the molecular weight and the location of the I block as well as on the molecular weight of the whole chain. For BIBs the tau-n were close to that for homopolyisoprene (homo-PI), with the molecular weight the same as BIBs. The loss curves of BIs and BIBs were much broader than that of homo-PIs. To analyze the behavior, we reduced the molecular weight, the molecular weight between entanglement, and the friction coefficient of the B block to those equivalent with the PI block. Using these reduced molecular weights, we can reasonably well explain the longest relaxation times tau-1, the nominal times tau-n, and the distribution of dielectric relaxation times by the bead-spring model or the tube model.