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Several hydrogels of N-vinylimidazole and sodium styrenesulfonate have been prepared by radical cross-linking copolymerization in aqueous solution, using N,N′-methylene-bisacrylamide as crosslinker. Depending on composition, these hydrogels were neutral, amphoteric, cationic or anionic. Compression-strain measurements were performed on samples as-synthesized and swollen in deionized water or in acid aqueous solutions, with and without salt. It was thus found that the cross-linking densities determined by compression measurements on as-synthesized samples are in good accordance with those calculated by means of the model of polymer networks with pendant vinyl groups. A non-Gaussian parameter (beta) was introduced to explain that the elastic moduli (G) of samples swollen at equilibrium are larger than predicted by the Gaussian model. The beta values of the neutral or ionized systems increase with swelling and fall into a single curve, which denotes a common behavior. Swelling has two opposite effects on G; on the one hand G decreases because the polymer volume fraction diminish and the system shifts from the affine limit to the phantom one; on the other, beta increases and contributes to increasing G. The balance of those two opposite effects determines the variation of G with swelling. The possible contribution of ionic crosslinks to nue for the polyampholyte and for the polycation wearing divalent counteranions was discussed. A peculiar system is poly(sodium styrenesulfonate), whose cross-linking density is much lower than expected.