An investigation into the performance of spherical-reflector antennas with Gregorian correctors is described with particular reference to their application in satellite-communications ground stations. Feeds comprising corrugated scalar horns propagatinga balanced HE11hybrid mode are considered, this choice eliminates cross-polarisation components of field in the spherical-reflector aperture. The theoretical performance of the spherical reflector with various subreflector profiles is estimated by using the aperture-field method to calculate the antenna-gain factor, far-field radiation pattern and overall efficiency as functions of the subreflector and feed positions. An optimum subreflector profile is chosen on the basis of maximum overall efficiency for a particular feed and antenna-scan angle. It is concluded that, for conventional scalar horns, the side-lobe level of the far-field radiation pattern is rather high, being about −11.5 dB with a corresponding gain factor of 0.85 and an overall efficiency of 0.65 for a scan angle of ±7°. Much lower side-lobe levels can be achieved, together with high gain factors, but only with lower overall efficiency. The spherical-reflector-antenna performance is compared to that of a front-fed paraboloid with the same feed and a higher efficiency is predicted for the former antenna. Preliminary consideration is given to the design of a dualmode feed so as to provide an additional tracking pattern, also to initial mechanical-design aspects.