The end-to-end performance of a dual-hop relaying system operating over independent, non-identical Nakagami-m fading channels, is analyzed and evaluated. Closed-form expressions for the cumulative distribution function, the probability density function, the moments and the moment generating function of the end-to-end signal-to-noise ratio (SNR), are derived. Using these results, closed-form expressions for the outage probability are presented for both channel state information and fixed-gain relays. Furthermore, for the case of fixed-gain relay, the average end-to-end SNR, the amount of fading and the average bit-error rate are also expressed in closed-form. The proposed mathematical analysis is complemented by numerical examples, including the effects on the overall performance of the SNRs unbalancing as well as the fading severity.