The propagation of electromagnetic waves is examined in inhomogeneous media where the product of the permittivity and permeability is independent of position. A plasma-like frequency dispersion of the refractive index in these media is predicted. It is established that there is a cutoff frequency below which electromagnetic waves cannot be excited in these media. In general, two types of inhomogeneous waves can propagate in these media: transverse electric and transverse magnetic. The magnetic field of the transverse electric waves has a longitudinal component and is elliptically polarized in the plane formed by the wave normal and the gradient of the parameters of the medium. The electric field of the transverse magnetic waves has similar properties.