Two　tuberculosis　(TB)　models　with　treatment　and　self-cure　are　investigated.　It　is　assumed　that　the　treated　individuals　may　reenter　either　the　latent　compartment　due　to　the　remainder　of　Mycobacterium　tuberculosis　or　the　infectious　compartment　due　to　the　treatment　failure.　On　the　other　hand,　infectious　individuals　with　mild　symptoms　may　reenter　the　latent　compartment　due　to　self-cure.　After　investigating　a　simple　model　with　one　latent　compartment,　a　TB　model　with　two　latent　compartments　is　studied　to　describe　the　slow　and　fast　progression　of　the　exposed　individuals.　The　basic　reproduction　numbers　of　those　two　models　are　defined,　and　their　epidemiological　interpretation　is　given.　Similar　threshold　dynamics　is　obtained　for　those　two　models:　the　disease　dies　out　ultimately　when　the　basic　reproduction　number　is　less　than　or　equal　to　one;　the　unique　endemic　equilibrium　is　globally　stable　when　the　basic　reproduction　number　is　greater　than　one.　The　influence　of　treatment　failure　and　self-cure　on　the　basic　reproduction　number　is　also　discussed.