  Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be
an $R$-module. For a non-negative integer $n$ it is shown that, if the sets
$\Ass_R(\Ext^{n} _{R}(R/I,M))$ and $\Supp_R(\Ext^{i}_{R}(R/I,H^{j}_{I,J} (M)))$
are finite for all $i \leq n+1$ and all $j< n$, then so is
\linebreak$\Ass_R(\Hom_{R}(R/I,H^{n}_{I,J}(M)))$. We also study the finiteness
of $\Ass_R(\Ext^{i}_{R}(R/I,H^{n}_{I,J} (M)))$ for $i=1,2$.
