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We investigate the effects of molecular opacities on the evolution of TP-AGBstars that experience the third dredge-up, i.e. with surface abundances ofcarbon and oxygen varying with time. To this aim, a routine is constructed toderive the molecular concentrations through dissociation equilibriumcalculations, and estimate the opacities due to H2, H2O, OH, C2, CN, and CO forany given density, temperature, and chemical composition of the gas. Then,synthetic TP-AGB models with dredge-up are calculated by either 1) adopting thenewly developed routine, or 2) interpolating between fixed opacity tables forsolar chemical composition, which is the usual prescription in AGB evolutioncalculations. The comparison between the two cases shows that the change in thedominant opacity sources, as the C/O ratio grows from below to above unity,crucially affects the evolution of the effective temperature, i.e. causing anotable cooling of the carbon-rich models (with C/O>1). From the comparisonwith observational data, it turns out that TP-AGB models with variablemolecular opacities are able to reproduce the observed range of effectivetemperatures, mass-loss rates, and wind expansion velocities of C-type giantsin the solar neighbourhood, otherwise failed if assuming fixed molecularopacities for solar-scaled mixtures. Finally, we mention other importantevolutionary and observational effects that result from the adoption of thevariable opacities, such as: i) significant shortening of the C-star phase dueto the earlier onset of the super-wind; ii) consequent reduction of the carbonyields; iii) reproduction of the observed range of near-infrared colours ofC-stars.Comment: 13 pages, 10 postscript figures, to appear in A&

Asymptotic Giant Branch evolution at varying surface C/O ratio: effects of changes in molecular opacities