The electronic response of self-doped graphene supported on metal substrates shows two well-distinct plasmon modes: the acoustic plasmon, characterized by a linear dispersion, and a nonlinear plasmon. The nonlinear plasmon originates from the anisotropy of the electron bands of graphene around the K point. The existence of two plasmons with a different dispersion relation demonstrates that charge carriers with different group velocity may coexist within the same band in epitaxial graphene.