Let R be a commutative Noetherian ring, a an ideal of R, and M, N two nitely generated R-modules. We prove that the generalized local cohomology modules Ht a(M;N) are a-co nite; that is, Exti R(R=a;Ht a(M;N)) is nitely generated for all i; t 0, in the following cases: (i) cd(a) = 1, where cd is the cohomological dimension of a in R. (ii) dimR 2. Additionally, we show that if cd(a) = 1 then Exti R(M;Ht a(N)) is a-co nite for all i; t 0.
