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The aim of the paper is presenting a very simple but reliable tool to reproduce the evolution of alluvial rivers worldwide, typically characterized by longitudinal profile concavity and downstream bottom fining. A zero dimensional, two-reach, two-grain size hydro-morphological model has been developed to simulate the long-term evolution of alluvial watercourses up to the present state, starting from the basin orogeny. Firstly, the model is described and tested against six hypothetic cases to show the quasi-stationary behaviour of profile concavity and bottom fining. Then it is applied to four real watercourses having diverse size, hydrological and morphoclimatic characteristics: the Adige, Ob, Parana and Zambezi rivers. These are characterized by a different "age", indicated by the estimated time elapsed from the last significant tectonic episode in their basin, ranging from 10 to 300 million years for the four cases. For all the simulated rivers it has been confirmed a satisfactory replication by the model of the measured slopes and concavity of the longitudinal profile in the present conditions. Unfortunately, only a limited comparison of the computed sediment fining in the downstream direction was possible, as very few information on spatially-distributed measured grain size composition along the studied river systems is available.