We study theoretically the dynamics of chemically crosslinked gels in binary solvents on the basis of the Flory-type model and nonequilibrium thermodynamics. We find with the aid of numerical integration of the evolution equation that an instability occurs in the gel upon changing the composition of the surrounding solution. This instability is caused by a marked difference of timescales between quick mutual diffusion of solvent molecules and slow deformation of the gel network. Profiles of solvent composition and network deformation are also described in some details.