The fluid dynamic behaviour of a reactive chemical in a stream can be greatly influenced by the presence of sorbing suspended particles. In this case, a kinetically controlled mass transfer is established between sorbed and dissolved phases and complex interactions emerge between fluid dynamical transport processes, sorption–desorption kinetics and chemical reactions. These conditions often occur in rivers, where both suspended sediment and reactive substances are frequently present. This paper deals with the important case in which the chemical reactions are nonlinear decay phenomena that often affect chemical or biological substances. A vertical two-dimensional mathematical model is formulated to take into account advection, turbulent diffusion, particle sedimentation, exchange kinetics between sorbed and dissolved phases, and decay. The decay is modelled for the case in which two different nonlinear decay reactions affect the dissolved and sorbed phases. The main result of the work is to obtain analytically a one-dimensional differential model of the vertically averaged concentration of the dissolved phase, this being conceptually similar to the classical advection–dispersion–decay equation. However, in this case we include the effects of (i) the kinetics with the phase sorbed by suspended particles and (ii) the influence of the two different decay processes. For this purpose, the multiple-scale method of homogenization is applied to the two-dimensional model. The resultant one-dimensional differential model shows how suspended load and decay phenomena affect the pollutant transport mechanisms to a great extent in a non-intuitive way and that the links are nonlinear. Some quantitative results show that these influences are, in general, not negligible.