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We introduce the notion of a Banach space containing an asymptotically isometric copy of ?'. A well known result of Bessaga and Pelczyiiski states a Banach space X contains a complemented isomorphic copy of ?' if and only if X* contains an isomorphic copy of co if and only if X* contains an isomorphic copy of ?Oo. We prove an asymptotically isometric analogue of this result.

Asymptotically isometric copies of ℓ^{∞} in Banach spaces and a theorem of Bessaga and Pelczynski