We consider the response of entangled four-arm polybutadiene star Solutions to steady shear and to startup of steady shear in the nonlinear shear-rate regime. Data are reported both for the shear stress, measured in a cone and plate geometry using a temperature controlled ARES rheometer, and for birefringence measured in a Couette device using two-color birefringence. These data are then compared with predictions from the Mead-Larson-Doi (MLD) and Graham, Likhtman, McLeish and Milner (GLaMM) models for linear chains, but with the reptation mechanism turned off as an "ad hoc" means of accounting for the effect of the immobile branch point in these systems. The results for both models are reasonable. However, with the Milner-McLeish model for chain length fluctuations included, the MLD model gives better results at the lowest shear rates where the deep retractions of the arms are a significant contributor to chain relaxation. On the other hand, the local implementation of convective constraint release (CCR) in the GLaMM model gives better predictions for higher shear rates between the inverse reptation and inverse Rouse times, where the CCR mechanism largely obviates any contribution of the deep arm retractions to the relaxation process. (C) 2009 The Society of Rheology [DOI: 10.1122/1.3160733]