An SIS epidemic model with a delay corresponding to the latent period was investigated.By means of constructing Liapunov functionals,some sufficient conditions for the local and global stability of the endemic equilibrium and the diseasefree equilibrium were obtained,respectively.When the delay increases above some threshold,the endemic equilibrium loses its stability and Hopf bifurcation occurs,i.e.,a family of periodic solutions bifurcates from the endemic equilibrium.The effect of the delay on the spread of disease was disclosed.