Two-way product-and-forward (PF) relay networks can provide lower asymptotic symbol-error rate (SER) than amplify-and-forward (AF) relay networks. In order to study the performance of PF relay networks over Rayleigh fading channels, the asymptotic SER expression of the PF relay networks is derived and analytical results show that PF relay networks have better SER performance than AF relay networks. Experimental results agree well with the analytical results. In order to enhance the SER performance of PF relay networks, a power allocation algorithm to minimize SER under total transmit power constraint is proposed. Simulations show that proposed algorithm can significantly enhance the SER performance.