Let R be a commutative Noetherian ring, a be an ideal of R and M be an R-module. In this article, we investigate the cofiniteness and weakly cofiniteness of local cohomology and generalized local cohomology modules. Among other things, we prove that if Exti R(R/a, M) is weakly Laskerian for all i ≤ dim M, then the R-module Exti R(N, M) is weakly Laskerian for all i ≥ 0 and for any finitely generated R-module N with SuppR(N) ⊆ V (a) and dim N ≤ 1. As a consequence, we show that if M is an Rmodule such that Hi a (M) is a-weakly cofinite for all i ≥ 0, then the R-module Hi a (N, M) is weakly Laskerian for all i ≥ 0 and for any finitely generated R-module N with SuppR(N) ⊆ V (a) and dim N ≤ 1.
