Today, free-space optical (FSO) communication in the presence of an eavesdropper is considered as an important topic in the current literature. In this paper, security issues are investigated for FSO wiretap channels. Novel closed-form solutions, both approximate and asymptotic, for the average secrecy capacity (ASC) are derived over gamma-gamma (GG) atmospheric turbulence channels with pointing errors. As a significant aspect, misalignment errors at the eavesdropper's receiver follow the Rice distribution in order to take into consideration the spacing between the legitimate receiver and the eavesdropper's receiver, which is modeled as a nonzero boresight displacement. It is concluded that a greater normalized beam width is required to reduce the loss produced by such attacks in the high signal-to-noise-ratio (SNR) regime. Analytical results are further verified by Monte Carlo simulation results.