Most non-associated organic and inorganic compounds are shown to obey the principle of corresponding states with regard to the orthobaric or saturated densities. The compounds are divided into two classes : one class containing those substances which behave like the perfect gases (Ar, Kr, Xe) with respect to this principle; the other consists of all other non-associated species. Each class follows its own temperature-density relation. These relations contain only two parameters, specific for the compounds : the critical temperature and a critical density, calculated from a reference density. For the liquids the useful range of reduced temperatures is between the triple point and about 0.96; for the gases from approximately 0.7 or 0.8 to 1. Average absolute percentage deviations in predicted liquid densities are about 0.7 % (less than 1 %) for some 150 compounds and in predicted gas densities less than 10 % for about 50 compounds. For practical applications the equations can satisfactorily be used to predict liquid densities within 1 %, starting from a given density at ambient temperature.