Let I, J be ideals of a commutative Noetherian ring R and lett be a non–negative integer. Let M be an R–module such that ExtR t(R/I, M) is a finite R–module. If t is the first integer such that the local cohomology module with respect to (I, J) is non– (I, J) –cofinite, then we show that HomR (R/I, Ht I,J(M)) is finite. Also, we study the finiteness of Ext R i(R/I, HtI,J (M)), for i=1, 2. In addition, for a finite R–module M, we show that the associated primes of HI,J t(M) have an equal grade, when t=inf {i|Hi I, J(M) ¹0}.