Let R be a commutative Noetherian ring, I an ideal of R and M a finitely generated R-module. It is shown that, whenever I is principal, then for each integer $i$ the set of associated prime ideals $Ass_R Ext^i_R(R/I^n , M)$, $n = 1, 2, . . . ,$ becomes independent of $n$, for large $n$.