A theoretical model is developed for predicting equilibrium alluvial channel form. The concept of greatest relative stability, achieved by maximizing resistance to ﬂow in the ﬂuvial system, is presented as the basis for an optimization condition for alluvial systems. Discharge, sediment supply (quantity and calibre) and valley gradient are accepted as independent governing variates. The model is used to deﬁne a dimensionless alluvial state space characterized by aspect ratio (W/d), relative roughness (D/d), and dimensionless shear stress (τ*) or, equivalently, channel slope (S). Each alluvial state exhibits unique values of Froude number and sediment concentration. The range of alluvial states for constant values of relative bank strength (parameterized by an apparent friction angle, ϕ′) forms a single plane in the state space (W/d, D/d, τ* or S). The scaling relations produced by the model are consistent with laboratory channels exhibiting a range of bank strengths, and with the behaviour of natural channels. Copyright © 2004 John Wiley & Sons, Ltd.