In this paper, we investigate the effect of forward/backward channel memory (statistical dependence in the occurrence of transmission errors) on ARQ error controls. To take into account the effect of backward channel errors in the performance analysis, we suppose some modified ARQ schemes that have an effective retransmission strategy to prevent the deadlock incurred by the errors on acknowledgments. In the study, we consider two modified go-back-N schemes with timer control and with buffer control, one modified selective-repeat scheme and one modified stop-and-wait scheme. By analytical and simulation results, we show how much the performance in throughput and delay of the modified ARQ schemes is affected by the degree of error burstiness when the forward and backward channels are governed by a first-order Markovian block error pattern. We also show that there exists a large difference between the performances with the burst and independent error cases.