The transport numbers of the macroion constituent in aqueous solutions of fullerenehexamalonic acid, C-66-(COOH)12, and its lithium, sodium, cesium, and calcium salts were determined by the indirect moving boundary method. By combining the transport data with the literature data for the electrical conductivity of the same solutions, the fraction of bound counterions to the fullerenehexamalonate macroion was calculated. It was found that about 20-40% of counterions are associated with the macroion in the concentration range from about 0.1 to 0.002 mol COO-/L. Consequently, under the influence of a potential field, these counterions move toward the anode as an integral part of the migrating macroion in opposition to the electrical field. Therefore, the absolute values of the macroion constituent transport numbers are relatively high. The experimental values of the fractions of bound counterions were compared with the theoretical predictions based on the solution of the Poisson-Boltzmann equation for the spherical cell model, and a reasonable agreement was obtained.