The notion of bisimulation equivalence has been introduced by D.M.R.Park. Informally, two processes are bisimilar if their possible behaviors have the same branching structure, i.e. any behavior of one system can be reproduced by the other system. In this paper, in order to get equivalence notions nicely adapted to peculiarities of event structures, we have introduced a number of variants of bisimulation notions which consider all the relations between event occurrences in the structures. Quite close connections between the introduced and existing equivalences have been shown.