  In this paper, we introduce the notions of Gorenstein weak injective and weak
flat modules respectively in terms of weak injective and weak flat modules,
which is larger than classical classes of Gorenstein injective and flat
modules. In this new setting, we characterize rings over which all modules are
Gorenstein weak injective. Moreover, we also discuss a relation between weak
cosyzygy and Gorenstein weak cosyzygy of a module, and the stability of
Gorenstein weak injective modules.
