Asymmetric stars provide a challenging test of the tube model, which has been successfully applied to both linear chains and symmetric star polymers. Previous work has shown that the tube model can be applied with some success to asymmetric stars in the linear viscoelastic regime. This work considers asymmetric polybutadiene stars in the nonlinear regime, where the shear flow plays a significant role in the response of the asymmetric star. In the nonlinear regime it is expected that convective constraint release will be the dominant relaxation mechanism for the asymmetric star polymers, as has been demonstrated for linear and symmetric star polymers. By using two-color flow birefringence, the shear stress and first normal stress difference as a function of shear rate for entangled asymmetric stars can be determined. The experimental results are then compared with a tube-based model that includes convective constraint release and are found to be in reasonable agreement.