In this paper, we study the secure communication performance of non-orthogonal multiple access (NOMA) communication systems with aerial eavesdroppers. Firstly, the ground-to-ground NOMA communications systems are considered wherein the near user is uniformly distributed in an inner disc and the far user is uniformly distributed in an outer ring within cell coverage of a base station at the center. A single eavesdropper is uniformly distributed outside the protected zone or multiple eavesdroppers are randomly dispersed and modeled as a three-dimensional (3D) homogeneous Poisson point process. Subsequently, the secrecy performance of the ground-to-air NOMA communications systems are investigated wherein the near user is uniformly distributed in an internal 3D spherical cap and the far user is uniformly distributed in an external 3D spherical cap. To enhance secrecy performance, a protected zone is introduced around the ground base station. Novel exact expressions for the secrecy outage probability (SOP) for both scenarios are derived. Finally, Monte Carlo simulation results are presented to validate the correctness of the derived analytical expressions and demonstrate the effects of system parameters on SOP of the considered system.