Summary: In this paper, robust adaptive output feedback control is studied for a class of discrete-time nonlinear systems with functional nonlinear uncertainties of the Lipschitz type and unknown control directions. In order to construct an output feedback control, the system is transformed into the form of a Nonlinear AutoRegressive Moving Average with eXogenous inputs (NARMAX) model. In order to avoid the non-causal problem in the control design, future output prediction laws and parameter update laws with the dead-zone technique are constructed on the basis of the NARMAX model. With the employment of the predicted future outputs, a constructive output feedback adaptive control is proposed, where the discrete Nussbaum gain technique and the dead-zone technique are used in parameter update laws. The effect of the functional nonlinear uncertainties is compensated for, such that an asymptotic tracking performance is achieved, whereas other signals in the closed-loop systems are guaranteed to be bounded. Simulation studies are performed to demonstrate the effectiveness of the proposed approach.