Input-output conformance (ioco) testing is a well-known approach to model-based testing. In this paper, we study the complexity of checking ioco. We show that the problem of checking ioco is PSPACE-complete. To provide a more efficient algorithm, we propose a more restricted setting for checking ioco, namely with deterministic models and show that in this restricted setting ioco checking can be performed in polynomial time. © 2014 Springer International Publishing Switzerland.