Cognitive radio (CR) with spectrum-sharing feature is a promising technique to address the spectrum under-utilization problem in dynamically changing environments. In this paper, the achievable capacity gain of spectrum-sharing systems over dynamic fading environments is studied. To perform a general analysis, a theoretical fading model called hyper-fading model that is suitable to the dynamic nature of CR channel is proposed. Closed-form expressions of probability density function (PDF) and cumulative density function (CDF) of the signal-to-noise ratio (SNR) for secondary users (SUs) in spectrum-sharing systems are derived. In addition, the capacity gains achievable with spectrum-sharing systems in high and low power regions are obtained. The effects of different fading figures, average fading powers, interference temperatures, peak powers of secondary transmitters, and numbers of SUs on the achievable capacity are investigated. The analytical and simulation results show that the fading figure of the channel between SUs and primary base-station (PBS), which describes the diversity of the channel, does not contribute significantly to the system performance gain. Copyright (c) 2011 John Wiley & Sons, Ltd.