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We investigate the propagation of surface waves along a spatially dispersive graphene sheet, including substrate effects. The proposed analysis derives the admittances of an equivalent circuit of graphene able to handle spatial dispersion, using a nonlocal model of graphene conductivity. Similar to frequency-selective surfaces, the analytical admittances depend on the propagation constant of the waves traveling along the sheet. Dispersion relations for the supported TE and TM modes are then obtained by applying a transverse resonance equation. Application of the method demonstrates that spatial dispersion can dramatically affect the propagation of surface plasmons, notably modifying their mode confinement and increasing losses, even at frequencies where intraband transitions are the dominant contribution to graphene conductivity. These results show the need to correctly assess spatial dispersion effects in the development of plasmonic devices at the low THz band.