ABSTRACTEndorheic basins are catchments with no hydrological connection with marine environments. They cover 20% of the Earth's surface, and are mostly located in arid regions. Their drainage networks converge to lakes, salt flats or alluvial plains, whose dynamics are strongly driven by precipitation, evapotranspiration and groundwater discharge, among other factors. Integrated surface drainage and the creation of whole drainage systems typical of open basins are commonly restricted in these regions. Interestingly, the fluvial basin morphology of endorheic basins has not been extensively studied, and a variety of quantitative morphological descriptors used in open basins have not been utilized in the geomorphic analysis of endorheic basins. The objective of this study is to better understand the basin morphology of endorheic river basins by using well‐known geomorphological properties and their variations across scales. For three basins in northern Chile we computed the following descriptors and the corresponding relevant scales: the cumulative distribution of contributing area, the horizontal shape of the basins (i.e. Hack's law, normalized Euclidean length, and sinuosity of the streams), slope–area relationship, Horton's ratios and drainage density. We detected several properties typically found in open basins, but certain features which seem to be unique to closed basins were also identified. In particular, we found that horizontal and vertical geomorphic features seem to be linked, which suggests that an independent treatment of these features may not be appropriate for closed basins. Similar results were found regardless of the basin area, which illustrates the relevant effects of features that are specific to these particular regions. It is expected that our findings will improve both the geomorphic assessment of these basins and hydrological modelling of surface water and groundwater. Copyright © 2013 John Wiley & Sons, Ltd.