The conductance of poly(anetholesulfonic acid) and its lithium, sodium, and cesium salts in water was measured in the range from c(m) approximate to 0.001 to 0.20 monomol/dm(3) and in the temperature range from T = 278 to 308 K. For the alkaline salts of poly (anetholesulfonic acid) Walden's rule is satisfied reasonably well, but not for the polyacid itself. For the sodium salt of poly(anetholesulfonic acid) we determined the concentration dependence of the polyion transference number at 298 K. From the measurements we calculated the fraction of free sodium ions, a, in the solution. The results were analyzed theoretically, using the expression alpha approximate to D+/D-0(+), where D+ is the self-diffusion coefficient of the counterion species. The cylindrical cell model and the Poisson-Boltzmann theory were used to calculate D+/D-0(+). The calculations are in good qualitative agreement with experimental data. These new measurements for polyanetholesulfonates were compared with the experimental results for poly(styrenesulfonic acid) and its salts obtained from the literature. The conductivities of aqueous solutions of poly(anetholesulfonic acid) and its salt are higher than the corresponding polystyrenesulfonate solutions. This can be explained by a smaller fraction of "free" (conducting) counterions in the latter case. This finding is consistent with thermodynamic data for these solutions as well as with the transference number measurements for sodium polyanetholesulfonate solutions presented here.