In this note, we study the H-infinity control problem for nonlinear descriptor systems governed by a set of differential-algebraic equations (DAEs) of the form Ex = F(x, w, u) z = Z(x, w, u), y = Y(x, w, u), where E is, in general, a-singular matrix. Necessary and sufficient conditions are derived for the existence of a controller solving the problem. We first give various sufficient conditions for the solvability of H-infinity control problem for DAEs. Both state-feedback and output-feedback cases are considered. Then, necessary conditions for the output feedback control problem to be solvable are obtained in terms of two Hamilton-Jacobi inequalities,plus a weak coupling condition. Moreover, a parameterization of, a family of output feedback controllers solving the problem is also provided.