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Two-way opportunistic relaying (TWOR) systems in amplify-and-forward (AF) strategy have been widely studied because of simplicity and high spectral efficiency. However, there have been few investigations into the performance of these systems. In this study, the authors present a performance analysis of the equal power allocation (EPA) scheme for the TWOR-AF systems over independent and non-identically distributed Rayleigh fading channels. Closed-form lower and upper bounds as well as an approximation of the outage probability are established to show the asymptotic performance of the EPA-TWOR-AF scheme, which are all tight at high signal-to-noise ratio. The diversity gain, coding gain and diversity-multiplexing tradeoff are obtained from the tight approximation. Using the moment generating function approach, a general symbol-error-rate expression in closed-form is derived for the EPA scheme with M-PSK or M-QAM modulation. Moreover, an instantaneous power allocation (IPA) scheme is proposed for the TWOR-AF systems, which significantly outperforms the EPA scheme in outage probability. The analytical outage probability and closed-form lower and upper bounds are also derived for the IPA-TWOR-AF scheme. Extensive simulation results are provided to validate the theoretical analysis.