Closing the loop around an exponentially stable single-input single-output regular linear system, subject to a globally Lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller, is shown to ensure asymptotic tracking of constant reference signals, provided that (a) the steady-state gain of the linear part of the plant is positive, (b) the positive integrator gain is sufficiently small, and (c) the reference value is feasible in a very natural sense. The class of actuator nonlinearities under consideration contains standard nonlinearities important in control engineering such as saturation and deadzone.