The star polymer samples were prepared by coupling narrow-distribution polystyryl anions with divinylbenzene and were characterized in terms of molecular weight, molecular weight distribution and coupling ratio. Dynamic viscoelastic properties of star-shaped polystyrenes having different molecular weights (M, = 1.3 20 x 10") and numbers (P= 7 39) of branches have been measured. The zero-shear viscosity '1o depends strongly upon the molecular weight at constant P, while it depends much less at constant M,. Molecular weight dependence of the steady-state compliance Je o are quite complicated. Je o increases with increasing molecular weight at constant P. When M, is constant, Je o is independent of molecular weight at P 7 and increases at P?. 7. Values of Je o are higher than those for the corresponding linear polymers. Relaxation spectra for star-shaped polystyrenes having many (P?. 15) branches exhibit a two-step change on the long-time side. These two sets of relaxation times are attributed to the relaxation mechanism associated with ordinary intermolecular entanglements and to that peculiar to branched polymers. The difference in the entanglement compliance for branched and linear polymers is smaller than that in Je o.