Abstract: he frequencydomain stahility of general asynchronous learning control system(ALC)is an alyzed, its modification with more strong stability condition,based on memory with forgetting factor andfeedback from E_(k+1)(s), is derived, the strict proof on related theorem and corollary is provided, and the geometric relationship between the learning matrix and the stability circle is discussed. Furthermore,an asymp-totic stability condition of ALC is obtained by using DNA method and some conclusions are given.