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This paper is concerned about the relation between local cohomology modulesdefined by a pair of ideals and Serre classes of R-modules, as a generalizationof results of J. Azami, R. Naghipour and B. Vakili (2009) and M. Asgharzadehand M.Tousi (2010). Let R be a commutative Noetherian ring, I, J be two idealsof R and M be an R-module. Let a\in \~{W}(I; J) and t \in N_0 be such thatExt^t_R(R/a,M)\in S and Ext^j_R(R/a,H^i_I;J(M))\inS for all i < t and all j>=0.Then for any submodule N of H^t_I;J(M) such that Ext^1_R(R/a;N)\in,we obtainHomR(R=a;H^t_I;J(M)/N)\inS.

On the local cohomology modules deffined by a pair of ideals and serre subcategories