Experimental cloud-point isotherms for polyethylene + hydrocarbon systems can exhibit abrupt changes in slope when the polyethylene has a broad molar mass distribution. Equations of state with parameters correlated to qualitatively reproduce this behavior can result in cloud-point curves that fold, crossing themselves. The point of self-intersection is the terminus of a three-phase region, with three liquid-like phases in equilibrium. Teardrop-shaped three-phase boundaries have been calculated using the Modified Sanchez-Lacombe (MSL) equation of state for polyethylene + ethylene and polyethylene + n-hexane systems. We also show some examples of phase boundaries separating two-phase regions from three-phase regions, which exhibit folding and self-intersection, indicating the presence of a region with four liquid-like phases in equilibrium. A boundary isolating a four-phase region inside a three-phase region has been calculated for a polyethylene-co-octene-1 + n-hexane system. It has been noted that the polyethylene molar mass distribution, especially the extension to high molar masses, determines whether three-phase regions and four-phase regions occur. (c) 2004 Elsevier B.V. All rights reserved.