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The paper contributes to the question whether the set of associated prime ideals of the local cohomology module HiI (M) is finite for all ideals I of a local ring (R, m) and a finitely generated generalized Cohen-Macaulay R-module M. We prove that it will be enough to solve the problem for i= 2 resp. 3 for ideals with two resp. certain ideals with three generators. This extends Hellus' result, see [5], of a Cohen-Macaulay ring. Moreover, in the case of M a Cohen-Macaulay module there is another sufficient criterion for the finiteness of associated prime ideals of HiI (M) related to certain cofiniteness conditions. Finally, we discuss several examples of the literature related to the problem.