The equilibrium swelling and phase behavior of monodomain nematic networks in nonmesomorphic solvents have been investigated as a function of temperature. The gels thermoreversibly undergo a phase transition between the swollen isotropic and shrunken monodomain nematic states with accompanying an anisotropic shape change. The nematic ordering occurs continuously within a narrow temperature range, which induces a significant reduction in gel volume as well as an elongation in the director direction. The length of the gels along the director axis in the nematic phase becomes larger than that in the isotropic phase, despite a considerable volume decrease upon nematic ordering. As temperature decreases, the shape anisotropy of the nematic gels increases without appreciable volume change, and becomes almost constant at the sufficiently low temperatures. A theory is proposed to describe the anisotropic swelling and phase equilibria of the monodomain nematic networks in isotropic solvents. The theory successfully describes the features of the swelling behavior observed.