Abstract: Establishing system equivalences for event structures such as trace and testing equivalences, require the observed actions to be exactly identical. However, an accurate measurement is impossible when interacting with the physical world, hence exact equivalence is restrictive and not robust. Using Baire metric, this paper proposes a generalized framework of event structures approximation by developing the notions of approximate interleaving (trace and singleton failures) equivalence and approximate step (trace and singleton failures) equivalence. The proposed framework captures the traditional exact equivalence as a special case. These approximate equivalences satisfy the transitive property, consequently, they can be successively used in event structures approximations.