The application of rigorous criteria for identifying fluvial style from sedimentary deposits is crucial if environmental reconstructions from stratigraphy are to be reliable. From modern observations, it appears that anabranching (anastomosing) rivers can be divided into separate humid and dryland classes. Each class has dissimilar characteristics to the other, necessitating different criteria for their recognition in the rock record. The criteria being used by sedimentologists to recognize deposits of anabranching rivers are derived solely from modern examples in humid regions, heavily biased to a few specific cases in Canada. These criteria are dominated by the concept of ribbon sandstone bodies encased in fine-grained floodplain sediment, with an overall low sand-to-mud ratio in the succession. There has been a general failure to appreciate that dryland anabranching rivers have significantly different characteristics to these and almost certainly leave a sedimentary record quite dissimilar to that previously expected.Avulsion or obtrusion (the gradual formation of an alternative channel) are the characteristic dynamic of anabranching rivers, forming and maintaining coexisting multiple anabranch channels. Avulsion or obtrusion require stream banks to have a high resistance to erosion, usually achieved by cohesive bank sediments or the reinforcement of banks by vegetative root mats. In some drylands, riparian vegetation can be sparse and bank resistance may depend in large part on a high clay content. Here, channel-fills are mud dominated and floodplains have a uniform fine-grained character which is usually structureless because of intense pedoturbation and some bioturbation. The evidence from such present-day dryland anabranching rivers suggests that their sedimentary record is likely to be one of laterally extensive mud-rich beds with weak or enigmatic fluvial indicators. Elsewhere, dryland anabranching systems are sand-dominated, their banks reinforced with riparian gallery forests sustained by infrequent flow and a shallow water table. Though the stratigraphy of these have barely been investigated, they are clearly different to humid-region anabranching systems, for their channels and islands are predominantly sandy. Anabranching rivers with prominent channel sandbodies separated by muddy islands have never been described from contemporary drylands. The interpretation of a dryland origin for ancient stratigraphic successions with this form is made, therefore, without evidence that they can actually exist. In the light of this, such interpretations should be re-evaluated.