Cellular wireless networks are an integral part of modern telecommunication systems. With the rapid growth of the number of cellular users and the scarcity of frequency spectrum, conventional cellular networks (CCNs) are facing difficulty in providing satisfactory service to users. To overcome the limitations of CCNs, an emerging architecture called the multihop cellular network (MCN) has gained a lot of attention. MCNs are emerging as a promising technology, benefiting from cellular and ad hoc network technologies. Multihop capability can be achieved in cellular networks by using relay nodes (RNs). For maximizing the benefit of multihop relaying, a good medium access control (MAC) layer scheme is required. In this work as a MAC scheme is proposed to meet the requirements of voice and World Wide Web (WWW) traffic in a multihop cellular network. In the proposed MAC scheme, the two classes of users (voice and WWW) contend with each other for resources based on class dependent permission probabilities. Fixed relaying technology is considered for multihop cellular networks. The performance of MCNs with voice traffic is quantified in terms of throughput, capacity, packet drop probability, power outage probability and packet interference probability. Two additional performance metrics are considered for WWW traffic: The average access delay per packet call and the average WWW packet transmission delay. The performance of the proposed MAC scheme in a multicellular system has been studied and compared with that of CCNs. The results indicate that MCNs with the proposed MAC scheme perform better than CCNs.