In a method and apparatus for fully automatic detection of anomalies in vessel structures, a 3D volume data set of an imaging 3D measurement of the vessel structure is obtained and, for an evaluation device, the vessel structure is detected in the 3D volume data set and subsequently is skeletonized in order to obtain a three-dimensional course of skeletonization paths. Characteristic quantities of the vessel structure are automatically determined along the skeletonization paths as features that are significant for an anomaly to be detected, in order obtain one or more feature series. The determined feature series are classified by non-linear imaging and comparison with reference feature series that have been determined for different classes of known vessel structures that contain different anomalies and known vessel structures without anomalies. Anomalies corresponding to the classification thus are identified.