The article studies the performance of cooperative multi-relay networks with random numbers of accessing users. A cooperative diversity is achieved at the destination nodes by receiving multiple independent copies of the same signal from M relays when all relays participate in the second phase of data transmission. The overall spectral efficiency (SE) of the considered system is investigated and accurate analytical expressions for it are developed. Furthermore, the article discusses how system performance is affected by its parameters. Monte Carlo simulations are used to validate the analytical results. The results revealed that increasing relays number on the network can improve the system performance. The results also indicated that there was improvement in the performance when the number of users increased. However, the performance dropped when this number became close the relays number.