[en] Let (R,m) be a Noetherian local ring and M a finitely generated R-module. The two notions of generalized regular sequence and generalized depth are introduced as extensions of the known notions of regular sequence and depth respectively. Some properties of generalized regular sequence and generalized depth, which are closely related to that of regular sequence and depth, are given. If x₁,... ,x_r is a generalized regular sequence of M then union_n1,...,nr Ass M/(x₁^n₁,... ,x_r^n_r)M is a finite set. Some finiteness properties for associated primes of local cohomology modules are presented. (author)