In this paper we propose two decentralized medium access control (MAC) schemes to coordinate the access of multiple transmitters adopting a Multi-Packet Reception (MPR) physical (PHY) layer. The proposed MAC schemes operate over an MPR-based PHY-layer and are divided into two stages. In the first stage the nodes indicate their willingness to transmit, while in the second one they jointly transmit. The MAC schemes differ by considering a Single-Packet Reception (SPR) or an MPR PHY-layer in the first stage. We analyze the throughput achieved by each MAC in a theoretical way. Several results obtained through simulation are also presented, which validate the numerical results obtained with the theoretical model. The results demonstrate the effectiveness of the proposed MAC schemes, and allow us to draw valuable conclusions about the design of distributed MPR systems.