The frequencies of optical modes of vibration in a metamaterial slab, contacting with vacuum, are investigated when the slab dielectric permittivity and the magnetic permeability show resonant behavior. Retardation effects are included in the no radiative zone. On the basis of the linear response theory, we calculate the components of the electromagnetic Green propagator. The dispersion curves and the corresponding power spectra are determined from the poles and the imaginary part of these components. Two sets of surface polaritonic frequencies are found for transversal electric TE- and transversal magnetic TM surface modes, corresponding to bonding and antibonding oscillations of the electric and magnetic fields at the slab surfaces. It is shown that for all the range of values in the relation between the resonance frequency of magnetic permeability and the resonance frequency of the dielectric permittivity there is one TE and one TM backward mode with negative group velocities. This parameter relation determines if the frequency range of TM modes can be separated from the corresponding interval for TE modes. Present work can be extended to consider waves in photonic crystals containing anisotropic slabs with resonant behavior in the optical properties, which can be useful to design omnidirectional optical filters.