We show some results about local homology modules and local cohomology modules concerning to being in a serre sub
category of the category of R-modules. Also for an ideal I of R we define the concept of CI condition on a serre category, which seems dual to CI condition of Melkerson . As a main result we show that for any minimax R-module M of any serre category S that satisifies CI (CI) condition the local homology module HiI(M)
(local cohomology module HIi(M) 2 S) for all i ≥ 0.