Surface plasma oscillations in metallic particles as well as in thin metallic films have been studied extensively in the past decades. New features regarding surface plasma excitations are, however, constantly discovered, leading, for example, to surface-enhanced Raman scattering studies and enhanced optical transmission though metal films with nanohole arrays. In the present work, the role of a metallic substrate is examined in two cases, one involving an overcoat of dielectric nanoparticles and the other an overcoat of metallic nanoparticles. Theoretical results are obtained by modeling the nanoparticles as forming a two-dimensional, hexagonal lattice of spheres. The scattered electromagnetic field is then calculated using a variant of the Green function method. Comparison with experimental results is made for nanoparticles of tungsten oxide and tin oxide deposited on either gold or silver substrates, giving qualitative agreement on the extra absorption observed when the dielectric nanoparticles are added to the metallic surfaces. Such absorption would be attributed to the mirror image effects between the particles and the substrate. On the other hand, calculations of the optical properties of silver or gold nanoparticle arrays on a gold or a silver substrate demonstrate very interesting features in the spectral region from 400 to 1,000 nm. Interactions between the nanoparticle arrays surface plasmons and their images in the metallic substrate would be responsible for the red shift observed in the absorption resonance. Moreover, effects of particle size and ambient index of refraction are studied, showing a great potential for applications in biosensing with structures consisting of metallic nanoparticle arrays on metallic substrates.