Handling inconsistencies in declarative process models (DPMs) has been of increased interest in previous years as even a single contradiction within a constraint set makes the entire DPM unsatisfiable. To support inconsistency detection and resolution, we provide a collection of generic inconsistency structures in this work. To this aim, we (1) iteratively identify inconsistency structures, (2) generalize them by analyzing their extendibility, (3) classify them based on their characteristics and (4) provide a visual representation of each generic structure. The resulting collection of structures provides the basis for future inconsistency detection and visualization approaches.