This paper analyzes the performance of a mobile multihop relay (MMR) system which uses intermediate mobile relay stations (RSs) to increase service coverage area and capacity of a communication system. An analytical framework for an MMR system is introduced, and a scheme for allocating the optimum radio resources to an MMR system is presented. It is very challenging to develop an analytical framework for an MMR system because more than two wireless links should be considered in analyzing the performance of such a system. Here, the joint effect of a finite queue length and an adaptive modulation and coding (AMC) scheme in both a base station (BS) and an RS are considered. The traffic characteristics from BS to RS are analyzed, and a three-dimensional finite-state Markov chain (FSMC) is built for the RS which considers incoming traffic from the BS as well. The RS packet loss rate and the RS average throughput are also derived. Moreover, maximum throughput is achieved by optimizing the amount of radio resources to be allocated to the wireless link between a BS and an RS.