To clarify the molecular mechanism of the counterion fluctuations in linear polyelectrolyte solutions, we have studied the dependence of the low-frequency electric birefringence relaxation on the degree of polymerization N and the monomer concentration C-p of sodium polystyrenesulfonate (NaPSS) in aqueous solution and the dependence of the low-frequency (LF) and high-frequency (HF) relaxations on the neutralization ratio a of polystyrenesulfonic acid (HPSS) in aqueous solution by the frequency-domain electric birefringence (FEB) method. The experimental results of the N and C-p dependence of the LF relaxation definitely show that the LF relaxation strongly depends on N but is weakly dependent on or almost independent of C-p, which indicates that the LF relaxation arises from the counterion fluctuation along the polyion. Also, it turns out from the experimental results of the a dependence of the LF and HF relaxations that the LF relaxation is ascribed to tightly bound counterions in the vicinity of a polyion and that the HF one is due to loosely bound counterions away from the polyion. These results support the molecular mechanism that the LF and HF relaxations come from the fluctuation of the tightly bound counterions along the polyion axis and from the fluctuation of the loosely bound counterions perpendicular to the polyion axis, respectively.