Non-binary type-II hybrid ARQ (HARQ), which combines shortened Reed–Solomon (RS) code with ARQ, is proposed. Its throughput is obtained by extending Lin and Yu’s analysis of binary type-II HARQ. The reliability and average delay are also obtained. The analytical results show that non-binary HARQ outperforms its binary counterpart in throughput, reliability and average delay when proper RS codes are selected. Non-binary HARQs are applied adaptively in a cellular phone system with uniformly distributed mobile terminals (MTs). MTs switch adaptively between two different hybrid schemes according to the average SNR of the received signals. The adaptive parameters include the size of the modulation constellation, the error-correction coding and their joint adaptation. Numerical results show that the adaptive scheme always outperforms its non-adaptive counterparts, and the adaptive modulation scheme is superior to adaptive coding and the joint adaptation scheme when the implementation complexity is a limiting factor. Robustness analysis shows that introducing a mixed modulation scheme in addition to QPSK and 8PSK in the adaptive modulation scheme is unnecessary, and HARQ with adaptive modulation is insensitive to deviations from the optimal threshold, thus facilitating its implementation. Copyright