This paper is concerned with the derivation of linear feedback closed-loop Stackelberg (LFCLS) strategies for a class of continuous-time two-person nonzero-sum differential games characterized by linear descriptor systems and the quadratic cost functionals. Compared with existing results, new sufficient conditions for the existence of a LFCLS strategy are obtained under less restrictive conditions. Furthermore, from the results of this paper, we also arrive at some conclusions about the linear-quadratic closed-loop Nash game for continuous-time descriptor systems. These conclusions are distinguished from those of the linear-quadratic closed-loop Nash game for state-space systems.