A class of an SIS epidemic model with delay，stagestructure and nonlinear incidence is established and analyzed. The existence of equilibrium points is discussed and its local asymptotic stability of equilibrium is discussed by the RouthHurwits and transcendental function zero distinction. Furthermore,the determinating theorem for the local asymptotic stability of this class of the epidemic is given, the conclusion provides some theoretical support for the disease control and prevention in the health sector.