Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences, and they typically involve the exchange of nonnegative quantities between subsystems or compartments, wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a neuroadaptive control framework for adaptive set-point regulation of discrete-time nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions.