Adaptive control schemes are developed for plants with unknown nonsmooth nonlinearities at both the input and output of a linear dynamics, New controller parameterizations with nonlinearity inverses for parameterized nonlinearities are employed, When implemented with true parameters and properly initialized, the inverse controller ensures closed-loop signal boundedness and output tracking, Adaptive laws are designed to update the parameter estimates to implement adaptive inverse controllers for unknown nonlinearities in two cases : the linear part known and the linear part unknown.