The NMR propagator technique allows the measurements of the variance σ(2)=<(ξ-<ξ>)(2)> of the displacements as a function of time t when flowing in a porous media. The time dependence of σ is a very sensitive test of Gaussian behavior compared to the analysis of the shape of the propagators. Superdispersion occurs when σ(2)[proportionality]t(α) with the exponent α larger than 1. In a homogeneous 30-μm grain pack and 10 < Pe < 35, we observed weak superdispersion in saturated conditions (α = 1.17) and gradually strong superdispersion as the water saturation decreases (up to α = 1.5) during steady-state oil-water two-phase flow. In saturated conditions, the corresponding longitudinal propagators and breakthrough curves are Gaussian or nearly Gaussian, whereas in two-phase conditions, the longitudinal propagators are nonsymmetric and the breakthrough curves show a tail at long times.