We augment retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to address a command-following problem for uncertain Hammerstein systems with possibly non-monotonic input nonlinearities. We assume that only one Markov parameter of the linear plant is known and that the input nonlinearity is uncertain. Auxiliary nonlinearities are used within RCAC to create a globally non-decreasing composite input nonlinearity. The required modelling information for the input nonlinearity includes the intervals of monotonicity as well as values of the nonlinearity that determine overlapping segments of the range of the nonlinearity within each interval of monotonicity.