We have studied the low- and high-frequency relaxations in polystyrene sulfonate solutions with different counterion species [X+ = H+, Li+, Na+, K+, (C4H9)(4)N+], from the frequency-domain electric birefringence (FEB) and the dielectric relaxation spectroscopies. The high-frequency (HF) relaxation frequency f(H) is proportional to the free intrinsic mobility, mu(o), of the counter-ion, whereas the low-frequency (LF) relaxation frequency f(L) is not proportional to mu(o). These different dependencies of f(L) and f(H) on the counter-ion species, support the notion that the LF relaxation arises from the fluctuation of counter-ions tightly bound in the vicinity of a poly-ion, in the direction parallel to the poly-ion long axis, and that the HF relaxation arises from the motion of counter-ions loosely bound away from the poly-ion in the direction perpendicular to the poly-ion axis. (C) 1999 Elsevier Science B.V. All rights reserved.