When the linear charge density of a polyelectrolyte chain reaches some critically high level, an electrostatic adsorption of part of the counterions appears, that is the so-called counterion condensation. There are contradictory opinions in the literature about the condensed counterion mobility along the polymer chain: the analytical theories predict some mobility, but the experimental research does not give an unequivocal answer. The present experimental investigation aims to verify the reports for the condensed counterion migration in a sinusoidal electric field. By using electric light scattering we investigate an aqueous suspension of γ-alumina particles after the complete adsorption of carboxymethyl cellulose on their surface; the probable migration of condensed counterions must contribute to the electric polarizability (when the frequency is under a given critical value) leading to a higher degree of particle orientation in the applied electric field. We compare the frequency dependences of the polarizability at two polyelectrolyte concentrations in the suspension: under and above the recharging point (appearing due to adsorption of the negatively charged polyelectrolyte on the positively charged surface) where the total polarizability is equal, but the ratio between the quantities of the diffuse and the condensed counterions is different. A procedure for determination of the counterion shares is invented; it uses the measured electrophoretic mobility and the calculated fraction of the condensed ions. The results indicate the absence of the polarizability component caused by the condensed counterions; i.e. they do not manifest their presence when an external electric field is applied. We have concluded that the condensed ions are immobile in a sinusoidal field with moderate intensity in the frequency range of 10 Hz to 1 MHz.