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Let {X, Xi;i≥1} be a sequence of i.i.d.r.v'.s, Z(t) =∑ti=1 Xi, t≥O.Consider the renewal process N(t) = inf{x; Z(x) > t}. In this paper we study the necessary moment conditions for {N(t);t≥0} approximating to Wiener processes.Our results have improv