This paper investigates the performance of the best relay selection, based on the max-min signal-to-noise ratio criterion for dual-hop free-space optical (FSO) full-duplex (FD) relays communication system. Decode-and-forward relays over log-normal (LN) channels for weak-to-moderate turbulence and gamma-gamma (G-G) channels for strong turbulence are con- sidered. We assume that the relays have full channel knowledge and the channel is symmetrical. Considering path loss effects and misalignment errors, the outage probability (OP) of the selection is obtained for both half-duplex (HD) and FD relays using the cumulative distribution function (CDF) of the best selection for LN and G-G random variables. Moreover, the average bit error rate (ABER) expressions for FSO communication system over LN channels are derived with the help of Gauss-Laguerre’s quadrature rule for HD relays, FD relays and direct link. Our results show that FD relays have lowest ABER and OP compared with the direct link and HD relays. Monte Carlo simulations corroborate the correctness of the obtained analytical results.