Abstract.We investigate the effects of molecular opacities on the evolution of TP-AGB stars that experience the third dredge-up, i.e. with surface abundances of carbon and oxygen varying with time. To this aim, a routine is constructed to derive the molecular concentrations through dissociation equilibrium calculations, and estimate the opacities due to H2, H2O, OH, C2, CN, and CO for any given density, temperature and chemical composition of the gas. Then, synthetic TP-AGB models with dredge-up are calculated by either adopting the newly developed routine, or interpolating between fixed opacity tables for solar chemical composition. The comparison between the two cases shows that the change in the dominant opacity sources, as the C/O ratio grows from below to above unity, crucially affects the evolution of the effective temperature, i.e. causing a notable cooling of the carbonrich models (with C/O> 1). From the comparison with observational data, it turns out that TP-AGB models with variable molecular opacities are able to reproduce the observed range of effective temperatures, mass-loss rates, and wind expansion velocities of C-type giants in the solar neighbourhood, otherwise failed if assuming fixed molecular opacities for solar-scaled mixtures. Finally, we mention other possibly important evolutionary and observational effects that result from the adoption of the variable opacities, such as: i) significant shortening of the C-star phase due to the earlier onset of the super-wind; ii) consequent reduction of the carbon yields; iii) reproduction of the observed range of near-infrared colours of C-stars.