Management of open-channel flow systems requires accurate models of flow transfer. This article presents a simple nonlinear model representative of the flow transfer in a river reach. The model is obtained through linearization of a physical model, simplification using the cumulant matching method and analytic identification of a nonlinear model coinciding with the linear model around equilibrium points, corresponding to the hydraulic permanent regimes. The methodology is illustrated on the diffusive wave equation and the Saint-Venant equations. The obtained nonlinear models are compared in simulation to the initial models. The nonlinear model is shown to ensure mass conservation, despite the variable delay element of the model. The proposed model can reproduce the nonlinear behavior of the time-delay with discharge variations. It is well-suited for fast simulations, flow forecasting, and for controller design.