The optical absorption spectra of two-dimensional (2D) arrays of spatially dispersivemetallic nanoparticles is examined. The corresponding non-local dielectric functionof the spheres is provided by (a) the hydrodynamic approximation and (b) theLindhard theory. More specifically, it is shown that the adoption of either types ofnon-local dielectric functions (hydrodynamic or Lindhard-type) for dilute 2Darrays of spheres does not alter the structure of the optical absorption spectrumbut leads to a blue-shift of all its distinct features. This effect becomes moreprominent as the radius of the nanoparticles decreases. However, for a close-packedarrangement of spheres, a non-local dielectric function provides a significantlydifferent optical spectrum than the local one, due to the dominant role of near-fieldeffects, which strongly depend on the choice of the dielectric function of the metal.