Abstract: Generally, controlled obstructions depend on a size parameter epsilon. Stability asserts that for sufficiently small epsilon, the epsilon obstruction group is isomorphic to the inverse limit of such groups as epsilon -> 0. (More precisely, the inverse system is Mittag-Lefler). Stability is important in geometric applications, and in particular stability for surgery obstructions is needed in the construction of exotic homology manifolds. Recently Ranicki and I have obtained a proof of stability for controlled simple surgery.