Let R be a commutative Noetherian ring, M be a weakly Laskerian R-module and be an ideal of R. Moreover, suppose that F and T are two covariant R-linear functors such that for each R-module L, FL and TL are -torsion for some ideal of R containing . In this article, we study the annihilators of the R-modules jFHi M and jTHi M, where for j 0, jF− (respectively, jT−) is the jth right (respectively, left) derived functor of F (respectively, T).
