Cloud-point curves by DSC measurements at different scanning rates on solutions of two samples of poly(vinyl methyl ether) in water show two minima in a temperature-composition plot. The significance of the data was confirmed by static measurements of the coexisting-phase compositions and phase-volume ratios. A thermodynamic analysis in terms of a strongly concentration-dependent interaction parameter leads to the conclusion that the system H2O/PVME exhibits so-called type III behavior. For polymers of infinite molar mass, such behavior is characterized by the occurrence of two off-zero critical concentrations, in addition to the usual zero critical concentration marking the Theta state.