An R-module M is called coretractable if Hom R (M/K , M) = 0 for any proper submodule K of M. In this paper we study coretractable modules and their endomorphism rings. It turns out that if all right R-modules are coretractable, then R is a right Kasch and (two-sided) perfect ring. However, the converse holds for commutative rings. Also, for a semi-injective coretractable module M R with S = End R (M), we show that u.dim( S S) = corank(M R ).2000 Mathematics subject classification: primary 16D10; secondary 16D40, 16L30.

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