In this paper, we analyze the performance of a two- way subcarrier intensity-modulated (SIM) amplify-and-forward (AF) relaying system over free-space optics (FSO) communication channels. The analysis takes into consideration attenuations due to atmospheric turbulence, geometric spread and pointing errors at the same time. We derive, in generalized infinite power series expressions, the tight upper and lower bounds of the overall outage probability and average probability of errors of the system. The study finds that this two-way subcarrier intensity- modulated AF relaying system using a binary phase shift keying (BPSK) modulation could be used for practical applications in case of a weak turbulence regime in which the required SNR is about 30 dB to obtain the average bit error probability of 10-6. It is also noted that the pointing errors clearly degrade the performance of the two-way subcarrier intensity-modulated AF relaying system.