An epidemic model of SIRS type with constant immigration of each class and distribution delay was dealt with by means of suitable Liapunov functions.In the absence of infectious individuals,the threshold of existence of endemic equilibrium was found.Below the threshold,the disease free equilibrium is globally asympototically stable;above the threshold,the disease free equilibrium is unstable and the endemic quilibrium is globally asymptotically stable.In the existence of input of infectious individuals,the models have no disease free equilibrium and the SIRS model is globally stable in the corresponding region.