Let $R$ be a Noetherian ring, $I$, $J$ two ideals of $R$, $M$ an $R$-module and $t$ an integer. Let $S$ be a Serre subcategory of the category of $R$-modules satisfying the condition $C_I$ and $\frak{a}\in \tilde{{\rm W}}(I,J)$. It is shown that if $\Ext_R^{j}(R/\frak{a}, H^{i}_{I,J}(M))\in S$ for all $i
