Fridy defined asypmtotic equivalence where x= (xk) and y= (yk) are real sequences and Pobyvanets obtained conditions for asypmtotic equivalence for a non-negative summability matrix. Marouf studied about asypmtotic equivalent sequences. Recently Gok, Nuray and Connor defined asypmtotic I-equivalent sequences where I is an ideal in the set of natural numbers N. The purpose of this paper is define asymptotic ?I- equivalence of two non-negative x= (xk) and y= (yk) sequences and study about ?I- regularity of an A = (ank) infinite matrix where ?x = (?xk) = (xk - xk+1).