A unified performance analysis is presented for dualhop amplify-and-forward (AF) relaying systems operating over non-identically distributed Rician fading channels. A general, two-parameter AF relaying model is used to cover various AF relaying schemes, namely, variable-gain AF relaying, fixedgain AF relaying, and channel-assisted relaying, as well other unconventional schemes. Although, in some applications, systems operating over Rician fading links can be approximated and analyzed using equivalent systems operating over Nakagami-m fading links, we show that this is not sufficiently accurate in the case of AF relaying systems. Therefore, single-fold infiniteseries expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous end-to-end received signal-to-noise ratio (SNR) of such systems are derived, and Monte-Carlo simulations are used to verify the precision of the derived expressions. In addition, the effects of the relaying model parameters, as well as the channel fading parameters, on system performance are studied.Index Terms-Amplify-and-forward, average symbol error probability, cooperative systems, dual-hop relaying, outage probability, Rician fading.