Abstract: Appell equation is a kind of important equations in analytic mechanics, which is not only suitable for holonomic systems but also applicable to nonholonomic systems. In order to study the stability of solutions of Appell equations, the gradient systems were extended to generalize gradient systems which contain the variable of time. Two kinds of generalized gradient systems were put forward and the characteristics of the systems were studied. The conditions under which Appell equations could be considered as one of two generalized gradient systems were obtained. Then, the stability of solutions of Appell equations were studied based on the characteristics of generalized gradient systems. Some application results show the feasibility.