The notion of a (generalized) inverse hypersystem in a category , that generalizes the known notion of a generalized inverse system, is introduced via a functor of a cofinally small weakly cofiltered category to . The appropriate morphisms are also defined such that they generalize the morphisms of generalized inverse systems. The corresponding category - is constructed such that - and - are subcategories of it. In comparison to the relationship between - and - , the essential benefit is that there exist inverse hypersystems which are not isomorphic to any generalized inverse system. The notion of a cofinite inverse hypersystem is also introduced, and it is proven that every generalized inverse hypersystem is isomorphic to a cofinite inverse hypersystem. At the end, it is shown by example how an inverse hypersystem could occur.