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To efficiently support tetherless applications in ad hoc wireless mobile computing networks, a judicious ad hoc routing protocol is needed. Much research has been done on designing ad hoc routing protocols and some well-known protocols are also being implemented in practical situations. However; one major imperfection in existing protocols is that the time-varying nature of the wireless channels among the mobile-terminals is ignored; let alone exploited. This could be a severe design drawback because the varying channel quality can lead to very poor overall route quality in turn, resulting in low data throughput. Indeed, better performance could be achieved if a routing protocol dynamically changes the routes according to the channel conditions. In this paper, we first propose two channel adaptive routing protocols which work by using an adaptive channel coding and modulation scheme that allows a mobile terminal to dynamically adjust the data throughput via changing the amount of error protection incorporated. We then present a qualitative and quantitative comparison of the two classes of ad hoc routing protocols. Extensive simulation results indicate that channel adaptive ad hoc routing protocols are more efficient in that shorter delays and higher rates are achieved, at the expense of a higher overhead in route set-up and maintenance.