This paper introduces the notion of endo-p-permutation kG-module. I give a characterization of indecomposable endo-p-permutation modules with vertex P via their source modules which are exactly the indecomposable endo-permutation modules whose classes in the Dade group D(P) are G-stable. In particular, when the normalizer of P controls p-fusion, I give a classification of sources of endo-p-permutation modules using the recent classification of the Dade group.