In　this　paper,　by　investigating　an　SIR　epidemic　model　with　nonlinear　incidence,　we　present　a　new　technique　for　proving　the　global　stability　of　the　endemic　equilibrium,　which　consists　of　introducing　a　variable　transformation　and　constructing　a　more　general　Lyapunov　function.　For　the　model　we　obtain　the　following　results.　The　disease-free　equilibrium　is　globally　stable　in　the　feasible　region　as　the　basic　reproduction　number　is　less　than　or　equal　to　unity,　and　the　endemic　equilibrium　is　globally　stable　in　the　feasible　region　as　the　basic　reproduction　number　is　greater　than　unity.　The　generality　of　the　technique　is　illustrated　by　considering　certain　nonlinear　incidences　and　SIS　and　SIRS　epidemic　models.