A direct method for transforming multiple solute transport equations, coupled by linear, series, and/or parallel first-order, irreversible reactions, into a series of simple transport equations having known solutions is developed. Using this method, previously published analytical solutions to single-species transport problems, in which the transported species reacts with first-order kinetics, can be used to derive analytical solutions to multispecies transport systems with parallel, serial, and combined reaction networks. This new method overcomes many of the limitations that were implicit in previously published methods. In particular, the number of species that can be described is unlimited, and the reaction stoichiometry does not have to be unimolar. To illustrate the method, an analytical solution is derived for a five-species serial-parallel reactive transport system. The analytical solution obtained for this problem is compared with a numerical solution obtained with a previously developed code. This analytical method is applicable to the verification of new numerical codes. ¿ 1999 American Geophysical Union