We have determined the (p, T, rho, x) phase boundaries in three mixtures of {(1 - x)CO2 + xC(2)H(6)) with x = (0.2516(6), 0.4924(5), and 0.7397(8)), in the vicinity of the critical locus from measurements of the relative dielectric permittivity epsilon(r). We combined accurate measurements of epsilon(r) with the Clausius-Mossotti relationship to determine the density. Measurements of epsilon(r) were made with two apparatuses : a reentrant cavity resonating at 375 MHz, and a coaxial cylindrical capacitor and bridge operating at a frequency of 1 kHz. The phase border was determined with uncertainties of approximately 0.5 per cent in density and 0.06 K in temperature, the latter corresponding to a fractional uncertainty of 1.2 . 10(-3) in pressure. The uncertainties in temperature and pressure resulted from the size of the temperature steps that were used; smaller values could be attained. The uncertainty in density resulted from uncertainty in the parameters relating the density to epsilon(r).