Cancer incidence rates for Swedish twins born between 1928 and 1965 and who both were alive at age 30 are studied by means of bivariate frailty models. Altogether, 7,280 fraternal (DZ) and 4,699 identical (MZ) twin pairs were followed up through December 31, 1995, for cancer status. The association between cancer incidence rates was statistically greater among the MZ than among the DZ pairs and stronger between women than between men; however, the magnitude of this association is relatively small and decreases over time. The relative decrease in dependency (association) is most easily detected using shared frailty models but may also be demonstrated, at least for women, using correlated frailty models. We also demonstrate that estimates of the correlation coefficient are similar when using any correlated frailty models derived from the power variance family but that these estimates disagree regarding the age at which the dependence is most important. The relative importance of dependence across age may sometimes be more interesting than the correlation coefficient itself. The latter may usually be estimated using alternative methods. Furthermore, when estimating correlation coefficients close to the boundary of the parameter space, simulation studies indicate that the correlated inverse Gaussian frailty model is more robust than the gamma frailty model.