Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R and M a fnitely generated R-module. We assume that N is a weakly Laskerian R- module and r is a non-negative integer such that the generalized local cohomology module Hia(M;N) is weakly Laskerian for all i < r. Then we prove that HomR(R-a;Hra(M;N)) is also weakly Laskerian and so Ass(Hra(M;N)) is finite. Moreover, we show that if s is a non-negative integer such that Extj Ext(M;Hia(N)) is weakly Laskerian for all i, j > 0 with i <s, then Ext^j(R-a;Hia(M;N)) is weakly Laskerian for all i< s and j >0. Also, over a Gorenstein local ring R of fnite Krull dimension, we study the question when the socle of Hna (N) is weakly Laskerian ?

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