A previously introduced method for predicting the properties of physical substances is described in detail and is given a mathematical justification. The method, here called the method of Analogous Series, requires only that the molecular structure of the target species be known and that the physical property of interest be known for several other species of known structure. It is shown to be very general and is successfully applied to the accurate prediction of pure-component properties (critical temperatures, liquid heat capacities), mixture properties (solution Henry constants, adsorption in zeolites, gas solubility in liquids, GC retention times), and to complex properties such as flash points. The relationship of the method to other predictive methods is discussed. The reference substance method is shown to be a special case of the Analogous Series method.