Based on stability theory for polydisperse fluid mixtures, expressions have been developed for the spinodal criterion, critical criterion and various stability tests for systems containing one discrete component and one continuous homologue. Each criterion can be separated into two parts: the first part is the same in form as that for binary systems; when we assume particular mixing rules for parameters of the equation of state, that part is determined only by the average molar mass of the homologue. The second part is concerned with the distribution function that characterizes the continuous component. To illustrate results, the van der Waals equation of state is used to calculate critical properties; the composition dependences of parameters a(1/2) and b of the van der Waals equation are assumed to be linear functions of molar mass. Numerical results for the critical loci are obtained. For a discrete component j and a continuous component j, systematic variations of parameters in the distribution function for j or of the interaction parameter n(ij) Show transitions between qualitatively different types of phase behavior.