This paper considers the hydraulic equations governing alluvial river dynamics. The shock-wave classes for this system were described and fully analysed by Needham & Hey (1991). The complementary expansion wave classes are determined in this paper. In addition, more general simple waves are considered and a weak-shock theory is established. This is used to consider several practical examples, including the dynamics of dredged river sections, the propagation of sediment slugs and the effects of sediment blocking and extraction.