We propose a theoretical testing framework and a test generation algorithm for concurrent systems specified with true concurrency models, such as Petri nets or networks of automata. The semantic model of computation of such formalisms are labeled event structures, which allow to represent concurrency explicitly. We introduce the notions of strong and weak concurrency: strongly concurrent events must be concurrent in the implementation, while weakly concurrent ones may eventually be ordered. The ioco type conformance relations for sequential systems rely on the observation of sequences of actions and blockings, thus they are not capable of capturing and exploiting concurrency of non sequential behaviors. We propose an extension of ioco for labeled event structures, named co-ioco, allowing to deal with strong and weak concurrency. We extend the notions of test cases and test execution to labeled event structures, and give a test generation algorithm building a complete test suite for co-ioco.