This paper studies the secrecy outage probability (SOP) of nonorthogonal multiple access (NOMA)-based integrated satellite-multiple unmanned aerial vehicle networks (ISMUAVNs) under nonideal hardware and colluding scheme. Colluding scheme is defined as that the eavesdroppers cooperate with each other to overhear the legitimate users’ signals. On this foundation, we obtain the closed-form expression for the SOP for the considered NOMA-based ISMUAVNs along with the partial unmanned aerial vehicle (UAV) selection scheme. To gain more things in the high signal-to-noise ratio (SNR) regime, we derive the asymptotic expression for the SOP, which gives fast ways to evaluate the benefit of the NOMA scheme and the impact of nonideal hardware impairments on the SOP. Finally, Monte Carlo simulation results are provided to show the correctness of the analytical results. In addition, with the help of representative results, some important and interesting findings are obtained.