Previous papers analyzed the throughput performance of the CDMA ALOHA system in Rayleigh fading channel, but they assume that the channel coefficient of Rayleigh fading was the same in the whole packet, which is not realistic. We recently proposed the finite-state Markov channel (FSMC) model to the throughput analysis of DS uncoded CDMA/unslotted ALOHA networks for fixed length data traffic in the mobile environment. We now propose the FSMC model to the throughput analysis of coded DS CDMA/unslotted ALOHA networks with variable length data traffic and one or two user classes in the mobile environment. The proposed DS CDMA/unslotted ALOHA wireless networks for two user classes with access control can maintain maximum throughput for the high priority user class under high message arrival per packet duration.