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In this paper, we present a novel approach for identifying argumentative discourse structures in persuasive essays. The structure of argumentation consists of several components (ie claims and premises) that are connected with argumentative relations. We consider this task in two consecutive steps. First, we identify the components of arguments using multiclass classification. Second, we classify a pair of argument components as either support or non-support for identifying the structure of argumentative discourse. For both tasks, we evaluate several classifiers and propose novel feature sets including structural, lexical, syntactic and contextual features. In our experiments, we obtain a macro F1-score of 0.726 for identifying argument components and 0.722 for argumentative relations.