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Three general theorems giving conditions for a radiating system to exhibit stationary polarization, stationary gain and the coincidence of stationary polarization and gain in a prescribed direction are presented. A necessary and sufficient condition for the polarization invariance of a circularly-polarized radiator is derived. The theorems are applied to a number of circularly-polarized sources and antennas which are broadly directional. The polarization change with respect to aspect for the radiators possessing a direction of stationary polarization at the pattern maximum is small; however, in the case of the helix, whose pattern maximum is not in the direction of stationary polarization, the change is comparatively large. The polarization variation which occurs when those antennas are used as the elements of an array or the primary feed of a reflector is considered.