  We define and study a class of entwined modules (stable anti-Yetter-Drinfeld
modules) that serve as coefficients for the Hopf-cyclic homology and
cohomology. In particular, we explain their relationship with Yetter-Drinfeld
modules and Drinfeld doubles. Among sources of examples of stable
anti-Yetter-Drinfeld modules, we find Hopf-Galois extensions with a flipped
version of the Miyashita-Ulbrich action.
