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We discuss an abstract semantics of concurrent systems generalising causal partial orders. The new semantics employs relational structures-called stratified order structures-which comprise causal partial orders and weak causal partial orders. Stratified order structures can be represented by certain equivalence classes of step sequences-comtraces-directly generalising Mazurkiewicz traces. We use Elementary Net Systems with inhibitor arcs as a system model and show that stratified order structures can provide an abstract semantics which is consistent with their operational semantics expressed in terms of step sequences. Two different types of operational rules are considered. We also construct occurrence nets to enable the generation of stratified order structures for a given run of the net.