The geometry of four meandering rivers has been investigated to detect linear and nonlinear links in their planimetry. To this aim, some robust nonlinearity tests-DVS plots, reversibility tests, and the Kaplan test-have been applied to the spatial series of local curvatures. The results are coherent and show that no relevant nonlinearities seem to be detectable in the analyzed meandering river patterns. From a river dynamics point of view, this can be explained by the occurrence of meander cutoffs and external forcing which prevent nonlinear morphodynamic processes from significantly influencing the long-term meandering dynamics and, consequently, the river geometry.