Molecular structure and rheological properties of ethylene-propylene (EP) random copolymer gels formed in toluene and methylcyclohexane, respectively, have been investigated by small-angle neutron scattering (SANS) and oscillatory shear. In both solvents, SANS results are analyzed by considering a fiberlike structure with a radius cross-section distribution function expressed by w(r) similar to r(-lambda). It is shown that a small change in the EP copolymer ethylene content has a large effect on the density of network connecting fibers but a much smaller effect on the diameter of the fibers. Oscillatory shear experiments reveal that the relaxation rate of the elastic modulus increases with decreasing EP copolymer ethylene content. This behavior indicates a decrease in the density of connections between fibers with decreasing ethylene content. The relationship between the elastic modulus and polymer concentration has also been examined. The results suggest, in light of the theory developed by Jones and Marques for rigid networks, that the rigidity of fibers formed in the gel is achieved only locally.