Multiple access relay systems with network coding provide spatial diversity with fewer transmissions. However, errors generated at the relay can propagate to the destination and the system performance can be severely degraded. Although many techniques have been proposed to resolve the error propagation, these techniques require some special operations at the relay or complicated reception schemes at the destination unless the global channel state information is available at the destination. This paper proposes a simple cooperative demodulation scheme for multiple access relay systems with network coding assuming that the relay simply forwards the decoded data and the destination has only the local channel state information.