A smooth concave configuration represents the most common quasi-equilibrium profile of alluvial rivers. In the present paper a generalized, unified set of models for the longitudinal profile of rivers is presented. Various independent effects that drive concavity in longitudinal rivers are considered and classified. The driving mechanisms considered here are (1) horizontal wavelike progradation of the river profile, (2) abrasion of bed particles, (3) aggradation of the river profile balancing subsidence at a constant speed, and (4) the effect of tributaries adding sediment and water to the main stem of the river. For simplicity it is assumed that the long-term supply of water and sediment is constant; hence a single discharge, that is, bank-full discharge, is used as an approximate characterization of the hydrologic regime for each point along the river. Sediment sorting has been studied elsewhere and is excluded from this analysis. The river is assumed to have uniform bed material, although the mean size may vary downstream. It is concluded that the quasi-equilibrium longitudinal profile created by each of the first three driving mechanisms mentioned above is concave. The degree of concavity varies, however, depending on a set of physical conditions that can be identified by a set of dimensionless numbers. A comparison of these numbers reveals the relative importance of the driving mechanisms for concavity. A condition for concavity driven by the fourth mechanism, that is, tributary input, is delineated. ¿ American Geophysical Union 1996