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Four realistic nonlinear models of pollutant transport with turbu-diffusion and reaction in rivers were studied. Exact solutions for all the kinetics models (no transport and no diffusion--the so-called stirred tank reactor) are described. An algorithm for calculating the rate constants from the exact solution is given. Exact solutions for all systems also are provided when transport terms are included with the kinetics (the plug flow model). The inclusion of turbulent diffusion prevents exact solution, but the methods or perturbation and the maximum (minimum) principle provide approximate solutions and bounds on the travelling wave solutions. The steady state is also analyzed by the bounding technique. These bounds, which may be used independently, demonstrate how the various parameters affect the solutions.