Melt rheological properties of different homologous series of linear polystyrenes (LPS) and randomly branched polystyrenes (RBPS) in both linear and nonlinear viscoelastic response regions are presented. In the linear regime, the master curves of the experimentally determined viscoelastic functions reveal that the temperature dependence of the shift factors ar for all the samples follow the Vogel-Tammann-Fulcher equation: a(T) proportional to exp[B/(T - T-0)] The value of the apparent activation energy B is found to increase slightly with an increasing degree of branching, reflecting a stronger temperature dependence of the viscosity of RBPS with respect to that of LPS. This difference is approached within the framework of both Ngai＇s coupling model and free volume theory. In the nonlinear regime, the shear rate dependence of the steady state viscosity eta( (gamma) over dot), corrected for both non-Newtonian and entrance effects, was measured. A comparison with the angular frequency dependence of the dynamic complex viscosity \eta*(omega)\ reveals interesting behavior concerning the Cox-Merz rule. In the non-Newtonian flow region, for LPS the relationship eta( (gamma) over dot) < \eta*(omega)\ is found to hold. On the other hand, RBPS exhibit an unusual failure of the rule characterized by the relationship eta( (gamma) over dot) > \eta*(omega)\. Elongational behavior of RBPS is also presented. Assuming a Wagner type single integral constitutive equation for the RBPS, a generalized time-temperature superposition principle in the field of nonlinear viscoelasticity is attempted: elongational stress curves measured at different temperatures are found to qualitatively match the same master curve if both the time and strain rate are reduced by an appropriate shift factor.