The viscosity of sodium polyacrylate (NaPAA) and poly(sodium 4-styrenesulfonate) (NaPSS) solutions was experimentally measured with various added salt (NaCl) concentrations at different temperatures. With a low salt concentration, the reduced specific viscosity (eta(rs)) exhibits a maximum and then a minimum with decreasing polyelectrolyte concentration (C-p) and diverges as C-p approaches zero. A new statistical mechanics model was developed based on the combination of Eyring's absolute-rate theory and Jiang's polyelectrolyte model. This model can satisfactorily correlate the viscosity of NaPAA and NaPSS solutions over the entire range of added NaCl concentration and temperature in this study and correctly predict the anomalous concentration-dependent behavior Of eta(rs).