Let R be a commutative Noetherian ring, a be an ideal of R and M be an R-module. The main purpose of this paper is to answer the Hartshorne's questions in the class of weakly Laskerian modules. It is shown that if s 1 is a positive integer such that Extj R(R=a;M) is weakly Laskerian for all j s and the R-module Hia (M) is FD1 for all i < s, then the R-module Hia (M) is a-weakly co nite for all i < s. In addition, we show that the category of all a-weakly co nite FD1 R-modules is an Abelian subcategory of the category of all R-modules. Also, we prove that if Exti R(R=a;M) is weakly Laskerian for all i dimM, then the R-module Exti R(N;M) is weakly Laskerian for all i 0 and for any nitely generated R-module N with SuppR(N) V (a) and dimN 1. 1.
