In this paper, we consider dynamical behaviors of an SIRI epidemic model with nonlinear incidence rate and delay siuation*. Firstly, By employing the Dulac function and the method of linearization of this equations of each equilibrium, we obtain the global stability of each equilibrium without delay. Secondly, by using the method of linearization of this equations, we prove the local stability of each equlibrium for the systems with delay. Finally, by Lyapunov functional we derive global stability of the disease-free equilibrium.(* Indicates a formula, please see the full text)