To increase modularity, aspect-oriented programming provides a mechanism based on implicit invocation: An aspect can influence runtime behavior of other modules without the need that these modules refer to the aspect. Recent studies show that a significant part of reported bugs in aspect-oriented programs are caused exactly by this implicitness. These bugs are difficult to detect because aspect-oriented source code elements and their locations are transformed or even lost after compilation. We investigate four dedicated fault models and identify ten tasks that a debugger should be able to perform for detecting aspect-orientation-specific faults. We show that existing debuggers are not powerful enough to support all identified tasks because the aspect-oriented abstractions are lost after compilation. This paper describes the design and implementation of a debugger for aspect-oriented languages using a dedicated intermediate representation preserving the abstraction level of aspect-oriented source code. We define a debugging model which is aware of aspect-oriented concepts. Based on the model, we implement a user interface with functionalities supporting the identified tasks, like visualizing pointcut evaluation and program composition.