A nonlinear dynamic compensator framework for Hammerstein systems with passive nonlinear dynamics is proposed. For this class of systems controlled by passive nonlinear dynamic compensators we prove global closed-loop stability by modifying the dynamic compensator to include a suitable input nonlinearity. The proof of this result is based on dissipativity theory and shows that the nonlinear controller modification counteracts the effects of the input nonlinearity by recovering the passivity of the plant and the compensator.