Nonlinear relaxation dynamics of highly entangled solutions of high molecular weight 1,4-polybutadiene (PB) in a PB oligomer are studied in steady shear and step shear flows. Polymer entanglement densities vary in the range 14 less than or equal to N/N-e(phi) less than or equal to 84, allowing systematic investigation of entanglement effects on nonlinear rheological response. In agreement with previous steady shear studies using well entangled polystyrene solutions, a flow regime is found where both the steady-state shear stress and first normal stress difference remain constant or increase quite slowly with shear rate, leading to a plateau in the steady-state orientation angle. The magnitude of the average orientation angle in the plateau range is in accordance with predictions of a recent theory by Islam and Archer (2001). In step shear, the nonlinear relaxation modulus G(t,gamma) is approximately factorable into time-dependent G(t) and strain-dependent h(gamma) functions only at long times, t > lambda(k), where lambda(k)approximate toO(tau(d0)). This finding is consistent with earlier observations for entangled polystyrene solutions; however the complex crossing pattern in G(t gamma)h(-1) (gamma) that precede factorability in the latter materials is not observed. For all but the most entangled sample, apparent shear damping functions h (gamma,t) = (G(t,gamma))/(G(t)) immediately following imposition of shear are in nearly quantitative accord with the damping function h(DEIA) predicted by Doi-Edwards theory.