The modes of wave propagation in media with a negative dielectric constant are not simple, unlike those for electromagnetic waves in media with a positive dielectric constant (where modes propagate inside the media with positive phase velocity since the refractive index is usually positive). Instead, they depend on the permeability sign, either positive or negative, and exhibit completely different features. In this report, we investigated a wave confined on the surface of a negative-dielectric constant and a positive-permeability plasma medium for which the refractive index is imaginary. The propagation mode is similar to surface plasmon polaritons on the metal containing free electrons, but its frequency band is different due to the significant spatial gradient of the dielectric constant and a different pressure term. We also studied a wave with a negative dielectric constant and negative permeability, where the refractive index is negative. This wave can propagate inside the media, but its phase velocity is negative. It also shares similar qualities with waves in plasmonic devices with negative permeability in the photon range. Published by AIP Publishing.