The concept of I-stable modules was defined by Tran Tuan Nam in (Tran, 2013) and the author used it to study about the representable of local homology modules. In this paper, we will introduce the concept of (,)IJ-stable modules, which is an extension of the I-stable modules. We study the (,)IJ-stable for local homology modules with respect to a pair of ideals, these modules have been studied in (Tran, & Do, 2020). We show some basic properties of (,)IJ-stable modules and use it to study the artinianess of local homology modules with respect to a pair of ideals. Moreover, we also give the relationship between the artinianess, (,)IJ-stable and the varnishing of local homology module with respect to a pair of ideals.