Low Earth orbit (LEO) satellite mega-constellations, composed of hundreds or thousands of LEO satellites, are being deployed to provide global coverage, creating new security vulnerabilities. Uplink satellite transmissions are vulnerable to attacks by adversaries including other satellites. The purpose of transmission security in satellite communications is to prevent transmissions from being detected and intercepted through enabling covertness and secrecy, respectively. On the one hand, covert communications techniques lower the probability of transmissions being detected, thus concealing the presence of the transmissions and therefore the transmitter. On the other hand, physical-layer security techniques enable secrecy by exploiting the randomness of the wireless channel to create a better channel between the transmitter and the legitimate receiver than between the transmitter and the adversary, thus allowing information to be transmitted which cannot be intercepted by the adversary. By allowing multiple satellites to also cooperate with each other by sharing and combining their received signals, the quality of the uplink can be improved, which allows the transmitter to lower its transmit power. This reduces the amount of transmitted energy that can be received by the adversary, thereby reducing their ability to reliably detect and intercept the transmissions. The aim of this dissertation is to propose and analyze the secrecy and covertness performance of physical-layer security and covert communications techniques, respectively, in cooperative LEO satellite mega-constellations, involving dynamic directional transmission and reception—including beamforming, beampointing, and combining—and power control—including adaptive power control and opportunistic power control.