Automatic repeat request (ARQ) is a widespread technique for error control in data communication systems. This research examines the performance of conventional ARQ schemes over fading channels. The basic Gilbert-Elliott two-state Markov model is used to represent these channels. This basic model is recursively extended to a 2$ sp{n}$-state Markov chain suitable for n-bit block codes. Using this 'Extended Gilbert-Elliot' model, an approximation of the throughput efficiency of the conventional ARQ schemes is derived. This approximation is particularly valid for slow fading channels. Furthermore, performance plots are obtained, showing the effects of channel fading on throughput efficiency: ARQ performance deteriorates with slower fading, or alternatively, higher channel memory. Consequently, frequency-hopped codeword transmission is explored, a technique by which channel memory can be reduced. Throughput performance of frequency-hopped ARQ systems is derived, which shows significant potential improvements over systems with no frequency hopping.

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