This note presents an explicit solution to the problem of disturbance attenuation with internal stability for discrete-time nonlinear descriptor systems. Both the static-state feedback and dynamic output feedback cases are considered. In particular, we characterize a family of Hinfin controllers solving the problem locally around a neighborhood of the origin. To do this, we first derive two stability criteria for discrete-time nonlinear descriptor systems, and then, a version of a bounded real lemma is also developed based on the concepts of dissipation inequality and differential game. After that, the results are used to derive the Hinfin control theory for nonlinear discrete-time descriptor systems. The approach taken is mainly algebraic, and hence is simple and clear.