Argumentative discourse contains not only language expressing claims and evidence, but also language used to organize these claims and pieces of evidence. Differentiating between the two may be useful for many applications, such as those that focus on the content (e.g., relation extraction) of arguments and those that focus on the structure of arguments (e.g., automated essay scoring). We propose an automated approach to detecting high-level organizational elements in argumentative discourse that combines a rule-based system and a probabilistic sequence model in a principled manner. We present quantitative results on a dataset of human-annotated persuasive essays, and qualitative analyses of performance on essays and on political debates.