Dielectric measurements on three dodecyloxy-substituted poly(p-phenylene terephthalate)s are presented and compared with dynamic mechanical measurements reported earlier. The results are interpreted on the basis of a molecular laminate model for the structural arrangement, i.e. main-chain layers separated by partially ordered side chains. Most of the observed relaxations are assumed to originate from side-chain motions. The low-temperature gamma relaxation around -160-degrees-C is ascribed to local MotiOns Of the CH2 units in the side chains. The beta relaxation around -35-degrees-C involves a cooperative motion of the amorphous parts of the side chains, while the beta* relaxation just above room temperature is supposed to occur mainly in the crystalline parts of the side chains. Although some main-chain motions may already be involved in the relaxations at lower temperatures, they fully account for the alpha relaxation observed around 120-degrees-C.