In this paper, a first approach towards H-infinity control of nonlinear descriptor systems is addressed. Based on a generalization of the bounded real lemma (BRL) it is shown how the H-infinity control problem can be generalized to a class of non-linear descriptor systems. This class is characterized by a standard (E, A, B, C) descriptor description, however, the A, B, C matrices are allowed to include nonlinear but bounded coefficients. This setup allows to incorporate recent results in self-scheduled H-infinity control of parameter-varying systems into the corresponding problem for descriptor systems. All results require only the solution of linear matrix inequalities (LMIs), i.e, the controller computation is possible by numerically sound techniques.