In this talk, we introduce the category of coefficients for Hopf cyclic cohomology. We see that this category has two proper subcategories whose the smallest one is the known category of stable anti Yetter-Drinfeld

modules. The middle subcategory comprised of those coefficients which satisfy a generalized SAYD condition depending on both the Hopf algebra and the (co)algebra in question. We introduce several examples to show that these three categories are different. This is a joint work with Bahram Rangipour and

Dan Kucerovsky.