Actuator components of gantry robots, such as reduction gears or clutches, typically have nonlinear characteristics such as dead zone, hysteresis, or backlash. Iterative learning control (ILC) is widely used to achieve the high accuracy of repetitive operations performed by such robots. These nonlinearities can severely limit the achievable accuracy. However, their impact on ILC is not well understood. This paper considers a discrete time system under a control delay along the sample trajectory and with input backlash. The method of vector Lyapunov functions for repetitive processes is applied to design an ILC law that ensures the convergence of the learning error. An example is given to demonstrate the effectiveness of the proposed ILC algorithm.