In this paper, we analyze dual-hop buffer-aided (BA) relaying in the context of Free Space Optical (FSO) communications. Based on a Markov chain analysis, we study the impact of full-duplexity (FD) and half-duplexity (HD) on the outage and delay performance of the three-node network. Results highlight that FD relaying concurrently reduces the outage and delay of the network while max-link HD relaying does not enhance the diversity order compared to buffer-free systems. Our analysis also highlights on the impact of the buffer size and relay position on the achievable performance levels.