This paper analytically study the performance of amply-and-forward (AF) serial relaying free-space optical (FSO) systems employing avalanche photodiodes (APD) in atmospheric turbulence modelled by the Gamma-Gamma distribution. The subcarrier binary phase-shift keying (SC-BPSK) signalling is assumed and at each relay node, an APD is used for signal detection and amplification. Closed-form expressions of outage probability and average bit error rate (BER) are analytically derived taking into account the impact of atmospheric turbulence and APD receiver noise by using the moment matching method. The analysis is verified by Monte-Carlo simulation and a good agreement between the analytical and simulation results is confirmed.