Many recent political events, like the 2016 US Presidential elections or the 2018 Brazilian elections have raised the attention of institutions and of the general public on the role of Internet and social media in influencing the outcome of these events. We argue that a safe democracy is one in which citizens have tools to make them aware of propaganda campaigns. We propose a novel task: performing fine-grained analysis of texts by detecting all fragments that contain propaganda techniques as well as their type. We further design a novel multi-granularity neural network, and we show that it outperforms several strong BERT-based baselines.