Interruption detection is a new yet challenging task in the field of speech processing. This article presents a comprehensive study on automatic speech interruption detection, from the definition of this task, the assembly of a specialized corpus, and the development of an initial baseline system. We provide three main contributions: Firstly, we define the task, taking into account the nuanced nature of interruptions within spontaneous conversations. Secondly, we introduce a new corpus of conversational data, annotated for interruptions, to facilitate research in this domain. This corpus serves as a valuable resource for evaluating and advancing interruption detection techniques. Lastly, we present a first baseline system, which use speech processing methods to automatically identify interruptions in speech with promising results. In this article, we derivate from theoretical notions of interruption to build a simplification of this notion based on overlapped speech detection. Our findings can not only serve as a foundation for further research in the field but also provide a benchmark for assessing future advancements in automatic speech interruption detection.