Abstract: I present a KAM theorem for presymplectic mappings. The theorem has an “a posteriori” format: given a Diophantine frequency $\omega$ and a family of presymplectic mappings, we show that if for some map in this family we can find an embedded torus which is approximately invariant with rotation $\omega$ and satisfies some non-degeneracy condition, then we can find an invariant embedded torus for some map in the family close to the original map.