In this paper, we study the secrecy performance of mixed radio-frequency (RF) - free space optical (FSO) systems by considering both RF and FSO eavesdropper attacks. More precisely, we shed light into the design of secure mixed RF-FSO relay networks by questioning two critical design problems: 1) What are the main parameters in the design of secure RF-FSO relay networks? 2) How can we improve the confidentiality of the optical information? To do so, we derive the secrecy outage probability and the probability of positive secrecy capacity performance for mixed RF-FSO relaying schemes under RF and FSO eavesdropper attacks, respectively. To justify the problem, we consider two general fading models, Nakagami-m at the RF side and exponentiated Weibull distribution at the FSO side. The results, which are validated with the Monte-Carlo simulations, show that both the location and the size of the photo-aperture is very important in the design of RF-FSO relay networks to enhance the secrecy performance of the overall system.