User stories (USs) are a widely used notation for expressing requirements in agile software development. A comprehensive understanding requires assessing not only individual USs, but also analysing the dependencies among them. Recent advances in AI open up new possibilities for automation. Therefore, this paper proposes an AI-based approach to analysing order dependencies. To achieve this, we first semi-formally define plain and hierarchical order dependency, which relate USs based on their actions on semantically equivalent or contained entities. Dependency analysis is realised using a modular, extensible pipeline. Our approach integrates various AI-based methods, including traditional NLP techniques and LLMs, to classify actions and analyse semantic relationships. To facilitate the evaluation process, we create a benchmark dataset comprising both expert-curated and real-world USs, containing 1.499 manually labelled dependencies. We then compare NLP techniques with transformer- and LLM-based methods for the individual analysis steps, evaluating the overall effectiveness and efficiency of our approach. Our results suggest that AI-based dependency analysis is feasible, especially when LLM-based methods are integrated. In realistic backlog settings, we obtain F$_2$ scores of 73% for plain and 89% for hierarchical order dependency. Our approach forms the basis for automated dependency analysis in requirements engineering and enables extensions to cover additional dependency types in the future.