In this paper, we consider optimal control problems for a class of nonlinear descriptor systems. A necessary condition which may be regarded as the maximum principle for descriptor systems is derived, and some problems related to this necessary condition, such as the continuity and differentiability of the hamiltonian in this necessary condition, the sufficient and necessary condition on linear descriptor systems, and so on, are discussed. Our results may include some ones in optimal control problems for conventional systems. Finally, an illustrative example is also given.