Based on discrete multicomponent stability theory, a new method has been developed to obtain analytical expressions for spinodal and critical-point criteria for polydisperse fluid mixtures. This method is based on a theorem following from the classical theory of stability. Coupled with constraints (e.g. mole-fraction balance), this theorem yields analytical stability criteria for several multicomponent systems : a system containing one homologous series; a system containing one homologous series and one discrete component; and finally, a system containing an arbitrary number of homologous series and an arbitrary number of discrete components. The calculation procedure is much simpler than that using the classical determinant method.