An investigation was carried out on the effect of molecular architecture on the dynamics of multigraft (MG) copolymers of polyisoprene (PI) and polystyrene (PS). MG copolymers with regularly spaced multiple grafts with trifunctional (combs), tetrafunctional (centipedes), and hexafunctional (barbwires) branch points were synthesized by anionic polymerization and studied by dielectric relaxation spectroscopy (DRS) and dynamic mechanical spectroscopy (DMS). The PI precursors were characterized by the presence of segmental and normal mode processes. The temperature dependence of the dielectric relaxation time for the segmental (tau(S)) and normal mode (tau(N)) process was of the Vogel-Fulcher-Tammann (VFT) type. In the entangled regime tau(N) scales with M-4.0. The major findings for the MG copolymers are as follows: (1) all MG copolymers are characterized by the presence of segmental and normal mode relaxation; (2) rs is independent of molecular weight and architecture; (3)tau(N) is slower in a MG copolymer than in its PI precursor; (4) tau(N) in a MG copolymer of a given architecture is not a function of the overall molecular weight or the number of branch points; (5) the difference between the normal mode relaxation time for a MG copolymer, tau(N(PIPS)), and its PI precursor, tau(N(PI)), defined as Deltatau(N) = tau(N(PIPS)) - tau(N(PI)), depends strongly on the molecular weight of the PS graft (M-PS). An explanation was offered for the reasons underlying the observed slowdown of the normal mode relaxation in MG copolymers vis-a-vis their PI precursors.