Let M be a module over a commutative ring R with non-zero identity. In this paper, for a pair of ideals  of R, we introduce the inverse limit of local homology  as follows:    for all  Also, we study some of its properties and analyze their structure, the vanishing, non-vanishing and Artinianness of  Moreover, there are some exact sequences concerning the inverse limit of local homology, among them a variant of Mayer-Vietoris sequence.

inverse limit; local homology; local cohomology; vanishing of inverse limit of local homology, linearly compact module.