Abstract: Simple exclusion procosses are important infinite particle systems. This model was proposed by Spitzer (1)and studied extensively by Spitzer and Liggett (2). On the basis of the model, Yan Shi-jian and Chen Mu-fa proposed generalized exclusion processes and obtained the construction of the processes. Zheng Wen-qu obtained a necessary and sufficient condition of the reversibility and proved that the set of the reversible probability measures of such a process is equal to the set of it's Gibbs states (3). This paper is devoted to the ergodic theory of a generalized simple exclusion proess with the state space {0, 1, …, m} (m ≥ 1, S is a countable set) and a reversible positive recurrent transition probability matrix P=(p(x, y))_x,y∈s Refering (4), the set of it's invariant probability measures is described and the ergodic properties of the process is obtained. We also prove that the set of it's reversible probability measures coinsides with the set of it's invariant probability measures. So the main re