It is demonstrated that the collapse of gels of radiation cross-linked poly(vinyl methyl ether) swollen in water is a truly discontinuous process obeying classic thermodynamic principles. The phenomenon can further be shown to be related to the relevant type of limiting critical demixing of solutions of the corresponding non-cross-linked polymer. There are three such types, including "classic" Theta behavior, and they can also be recognized in the swelling behavior of the cross-linked analogue.