The swelling behavior of a series of strong polyelectrolyte hydrogels based on N-isopropylacrylamide (NEPA) and 2-acrylamido-2-methylpropane sulfonic acid sodium salt (AMPS) was investigated in aqueous solutions of poly(ethylene glycol)s (PEG) of molecular weights 300 and 400 g/mol. Non-ionic hydrogels or hydrogels with 1 mol-% AMPS deswell with increasing PEG-300 volume fraction phi in the external solution up to phi = 0.6. As phi is further increased, the hydrogels start to swell up to phi = 1. The distribution of PEC inside and nut side the Eel phase changes with the gel volume PEG chains first move from the gel to the solution phase from phi = 0 to 0.6, while at higher phi values they again penetrate the gel phase. In PEG-400 solutions, the contraction of the gels is jumpwise first-order phase transition at a critical phi, while their reswelling occurs smoothly at higher values of phi. Calculations using the Flory-Huggins theory indicate attractive interactions between PEG and PNIPA segments, which are responsible for the observed reentrant transition behavior.