In this work, we apply argumentation mining techniques, in particular relation prediction, to study political speeches in monological form, where there is no direct interaction between opponents. We argue that this kind of technique can effectively support researchers in history, social and political sciences, which must deal with an increasing amount of data in digital form and need ways to automatically extract and analyse argumentation patterns. We test and discuss our approach based on the analysis of documents issued by R. Nixon and J. F. Kennedy during 1960 presidential campaign. We rely on a supervised classifier to predict argument relations (i.e., support and attack), obtaining an accuracy of 0.72 on a dataset of 1,462 argument pairs. The application of argument mining to such data allows not only to highlight the main points of agreement and disagreement between the candidates' arguments over the campaign issues such as Cuba, disarmament and health-care, but also an in-depth argumentative analysis of the respective viewpoints on these topics.