We present a theory of coupled fluctuations of polymer segments, counterions, and coions in semidilute polyelectrolyte solutions containing added salt. The coupling among the three species results in three relaxation modes, instead of the previous common usage of only two relaxation modes by absorbing the role of salt as an effective solvent. Among the three modes, one is the nondiffusive plasmon mode and the other two are diffusive modes. These three modes are unrelated to any other slow mode that may arise from effects such as aggregation. Explicit expressions are derived for the decay rates in terms of concentrations of polyelectrolyte and salt, and the degree of ionization of the polymer. The specific values for the decay rates of the three modes are shown as an illustration for a chosen set of values of experimental variables. In the absence of added salt, the present theory reduces to the previous theory of fast diffusion in salt-free polyelectrolyte solutions and to the Nernst-Hartley theory for simple electrolytes. (c) 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1263-1269