We present an enrichment of the Hateval corpus of hate speech tweets (Basile et al., 2019) aimed to facilitate automated counternarrative generation. Comparably to previous work (Chung et al., 2019), manually written counter-narratives are associated to tweets. However, this information alone seems insufficient to obtain satisfactory language models for counter-narrative generation. That is why we have also annotated tweets with argumentative information based on Wagemans ( 2016), that we believe can help in building convincing and effective counter-narratives for hate speech against particular groups.We discuss adequacies and difficulties of this annotation process and present several baselines for automatic detection of the annotated elements. Preliminary results show that automatic annotators perform close to human annotators to detect some aspects of argumentation, while others only reach low or moderate level of inter-annotator agreement.