Abstract: Two kinds of generalized gradient systems,namely generalized skew gradient system and generalized gradient system with symmetric negative definite matrix,are proposed,and the properties of these two kinds of generalized gradient systems are studied.The conditions under which the Tznoff equations can be considered as one of the two generalized gradient systems are obtained.The characteristics of the generalized gradient systems can be used to study the stability of solution of the Tznoff equations,and the conditions for the solution to be stable,asymptotically stable and unstable are given.Some examples are used to illustrate the application of the results.