A comprehensive river water-quality model, deterministic in type, is described in Part 1 and its application to a river catchment is given in Part 2, for which there is a separate abstract. The eleven processes represented in the model include nitrification, denitrification, photosynthesis, BOD decay, re-aeration and others, the rate equations for each being detailed, as well as the numerical integration employed to solve these. A choice of FORTRAN computer programs is available, each embodying the model—one being for “interactive” use from a computer terminal, one for conventional “batch” use at any computer centre, while a third form is envisaged for incorporation in a minicomputer or microprocessor controlling remote automatic water-quality monitoring stations. This third form would allow predictions of downstream quality immediately data are received from each station, so enabling early warning of impending substandard conditions.