A 24-hour or all-day coverage area (ADCA) is defined as the area within which it is possible, at any time and under a given weather condition, to establish a link with at least one of the satellites in the same orbit. The authors present a very efficient algorithm for locating ADCAs for satellites in geosynchronous orbit with a nonzero inclination angle. They explore some satellite link budget computations which relate to the satellite coverage problem through a single parameter, and thus simplify the checking condition to an inequality. A few useful properties of ADCA are first derived and applied to develop a rapid algorithm. Some related coverage problems are considered.