The conductivity behaviour of polyelectrolytes in very dilute solutions has been investigated. It is in general not possible to extrapolate the equivalent conductivity, Λ, to infinite dilution, primarily because the solvent conductivity, κ0, is affected by the polyelectrolyte. However, from the slope of the conductivity against concentration curve it is possible to determine the limiting equivalent conductivity, Λ°, which characterises the conductivity in a concentration region where the interionic interactions are limited to interactions between the polyion and its counter-ion atmosphere. Conductivity measurements were carried out with polyacrylic acid and carboxymethylated hydroxyethyl cellulose. Of the latter polyelectrolyte, samples with widely differing charge densities were used. From measurements performed with the sodium and potassium salts of the polyacids the limiting equivalent conductivity and friction coefficient of the polyions were determined. The experimental results in general did not conform to current polyelectrolyte theories and there was no direct evidence of counter-ion condensation in polyelectrolytes of high charge density.