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We propose two relay selection schemes for analog network coding (ANC) OFDM systems. One uses OFDM Symbol-Based Max-Min-Min Selection Criterion (OSBM3SC) to select only one relay for signal transmission, and the other uses a Subcarrier-Based Max-Min Selection Criterion (SBM2SC) to select multiple relays for signal transmission. Assuming a frequency-domain fully-uncorrelated Rayleigh fading channel, we derive the asymptotic symbol error rate (SER) performance for both schemes, and show that they both can achieve full diversity. Using extensive simulations, we further show that the presented analytical results are useful to accurately predict the high SNR error performance of practical OFDM systems.