Two branched polystyrene melts with narrow molar mass distribution have been synthesized: a multiarm A(n)-C-C-A(n) pom-pom polystyrene and an A(n)- C asymmetric star polystyrene where n is the number of arms. The pom-pom and the asymmetric star have molar masses of M-w = 300 kg/mol and M-w = 275 kg/mol, respectively. The pom-pom was estimated to have 2.5 arms on average, while the estimate is 3.3 for the asymmetric star. The molar mass of each arm is about 27 kg/mol. The melts were characterized in the linear viscoelastic regime and by elongational rheometry in the nonlinear regime. For asymmetric star polystyrene, the measured transient elongational viscosity is not consistent with a rheological constitutive equation that is separable in time and strain. Contrary to this situation, however, for pom-pom polystyrene, the transient elongational viscosity may be described by a time-strain separable constitutive equation for elongation rates larger than the inverse reptation time. Up to a Hencky strains of 2.6, the corresponding stress tensor component for the pom-pom is closely approximated by a model that assumes the arms to be fully relaxed while the cross-bar is part of an unrelaxed entanglement network model. At Hencky strains above 2.6 a saturation of stress occurs that we interpret as withdrawal of the arms into the cross-bar tube. The observed strain associated with arm withdrawal is significantly larger than that predicted from an equilibrium force balance on the branch points while it corresponds well with an estimate of the maximum stretchability of the cross-bar. At the highest elongation rate investigated, the transient elongational viscosity for pom-pom went through a reproducible maximum as a function of time.