A series of strong polyelectrolyte hydrogels was prepared from the sodium salt of 2-acrylamido-2-methylpropane sulfonic acid (AMPS) as the monomer and N,N'-methylene(bis)acrylamide (BAAm) as a crosslinker. The hydrogels prepared between 9 and 50 mol % BAAm appeared homogeneous to eye but exhibited large spatial fluctuations of polymer concentration, as determined by the light scattering measurements. The elasticity tests show that the modulus of elasticity of gels increases with increasing degree of swelling, starting from the gel preparation state. Thus, the mechanical properties of the hydrogels are improved on their swelling in water. It was shown that the hydrogels even at a gel state just after their preparation are in the non-Gaussian regime due to the high degree of spatial gel inhomogeneity.