We have calculated fundamental and overtone CH-stretching vibrational band frequencies and intensifies of neutral and cationic naphthalene and anthracene, the smallest of the polycyclic aromatic hydrocarbons. The calculations use a simple anharmonic oscillator local mode model with local mode parameters obtained from scaled ab initio calculations and ab initio calculated dipole moment functions. The ab initio calculations were performed at the self-consistent-field Hartree-Fock and the B3LYP hybrid density functional levels of theory with the 6-31G(d) and 6-311+G(d,p)basis sets. The Vapor phase overtone spectra of anthracene and both cations have not yet been observed. We find that the cation frequencies are blue shifted and the overtone transitions are of comparable intensities to those in the neutral molecules, contrary to the fundamental transitions which are significantly weaker in the cations. The method presented here can provide an accurate estimate of CH-stretching overtone spectra of neutral and cationic polycyclic aromatic hydrocarbons.