The asymptotic stability of the solutions of the differential equation x00 +h(t)x0 +x =0 is investigated under the restrictions that h(t) =2hn≯0 on[tn; tn+n], and h(t) = 0 elsewhere, lim n 1 tn = 1 and tn+1 - tn is not necessarily a multiple of, n 2 N .