In this paper, we analyze economic model predictive control schemes without terminal constraints, where the optimal operating behavior is not steady-state operation, but periodic behavior. We first show by means of a counterexample, that a classical receding horizon control scheme does not necessarily result in an optimal closed-loop behavior. Instead, a multi-step MPC scheme may be needed in order to establish near optimal performance of the closed-loop system. This behavior is analyzed in detail, and we show that under suitable dissipativity and controllability conditions, desired closed-loop performance guarantees as well as convergence to the optimal periodic orbit can be established. (C) 2016 Elsevier Ltd. All rights reserved.