Let a be an ideal of a commutative Noetherian ring R with non-zero identity and let N be a weakly Laskerian R-module andM be a finitely generated R-module. Let t be a non-negative integer. It is shown that ifHi a(N) is a weakly Laskerian R-module for all i < t, then HomR(R/a,Hta (M,N)) is weakly Laskerian R-module. Also, we prove that Exti R(R/a,Hta (N)) is weakly Laskerian R-module for all i = 0, 1. In particular, if SuppR(Hi a(N)) is a finite set for all i < t, then Exti R(R/a,Hta (N)) is weakly Laskerian R-module for all i = 0, 1.
