In this work, we study the secrecy performance of a mixed radio frequency-free space optical (RF-FSO) transmission systems. All RF links experience Nakagami-m fading and the FSO link experiences the Gamma-Gamma fading. The effect of pointing error and two types of detection techniques (i.e., heterodyne detection and intensity modulation with direct detection) are considered. We derive closed-form expressions for lower bound of the secrecy outage probability (SOP) and exact average secrecy capacity (ASC). Furthermore, by utilizing the expansion of Meijer's G-function, asymptotic results for SOP and ASC are derived when the electrical signal-to-noise ratio of the FSO link tends to infinity. Numerical and Monte-Carlo simulation results are provided to verify the accuracy of our proposed results.