The stress dependencies of the steady-state viscosity eta and, particularly, that of the steady-state elastic compliance J(e) of various linear isotactic polypropylenes (PP) and one long-chain branched PP are investigated using creep-recovery tests. The creep stresses applied range from 2 to 10,000 Pa. In order to discuss the stress-dependent viscosity eta and elastic compliance J(e) with respect to the influence of the weight average molar mass M-w and the polydispersity factor M-w/M-n the PP are characterized by SEC-MALLS. For the linear PP, linear steady-state elastic compliances J(e)(0) in the range of 10(-5)-10(-3) Pa-1 are obtained depending on the molar mass distribution. J(e)(0) of the LCB-PP is distinctly higher and comes to lie at around 10(-2) Pa-1. J(e)(0) is found to be independent of M-w but strongly dependent on polydispersity. eta and J(e) decrease with increasing stress. For the linear PP, J(e) as a function of the stress tau is temperature independent. The higher M-w/M-n the stronger is the shear thinning of eta and the more pronounced is the stress dependence of J(e). For the LCB-PP, the strongest stress dependence of eta and J(e) is observed. Furthermore, for all PP J(e) reacts more sensitively to an increasing stress than eta. A qualitative explanation for the stronger stress dependence of J(e) compared to eta is given by analyzing the contribution of long relaxation times to the viscosity and elasticity.