The development of a new local-mode model for the analysis of the overtone spectra of complex polyatomic molecules is described and is tested here with the simple linear triatomics HCN and DCN. Morse oscillator potential functions are used for the CH(D) and CN bonds, together with a Morse-like interbond coupling term. The novelty lies in our treatment of this interbond coupling term, which we believe to be more realistic than the widely used model of harmonically coupled anharmonic oscillators. The Hamiltonian is transformed to a basis of harmonic oscillator states and treated by perturbation theory to third order to yield an effective vibrational Hamiltonian matrix which is block-diagonal in the total excitation quantum number. The model contains five parameters relating to the stretching potential-energy surface which are refined in least-squares fits to the available spectroscopic data. Also a simple bond dipole model is used to estimate the intensities of the overtone bands within a given manifold of CH and CN vibrational levels. Comparisons with the previously determined quartic anharmonic force field of HCN and recent variational calculations on an ab initio potential surface reveal that our model captures the essential features of the stretching potential surface which determine the band origins and integrated band intensities of the HCN and DCN stretching vibrational overtones. Some new data on the band centres and integrated intensities of DCN are presented.