We formulate a mathematical model for infectious diseases that progress through distinct stages within latent hosts. A typical example of the disease is Tuberculosis (TB). For a general n-stage stage-progression (SP) model with bilinear incidence, our analysis of the global dynamics of the model depends on the basic reproduction number If then the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If then the unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region and the disease persists at the endemic equilibrium.