The current state of political science as a science of adjusting and diversifying the theoretical and methodological basis is characterized by some domestic and foreign researchers and experts as a crisis and (or) uncertain. This is due to the updating of the request regarding reproduction mechanisms formulation and scientific knowledge verification, which are adequate to the existing political trends (developing extremely dynamically and substantively). In turn, this explains the timeliness and targeted clarification of the adopted methods of political science research. In this sense, the problematic nature of determining a suitable research methodology is associated, firstly, with the borrowing of most of the theoretical positions and methodological attitudes from related disciplines (mainly from philosophy and sociology), and secondly, with the continuity of development (change) of the object under study, while not excludes indeterminism and inversion of modern science as such. The plane of political risks and opportunities of the modern world order raises the question of determining the adaptive and applied features of political science methodology in the context of fragmentation and co-evolution of the modern scientific picture of the world into a different quality of understanding and argument. Based on the understanding of the need to formulate a methodological toolkit for researching the positioning of the US president in the global political process, the authors determine the appropriateness of using the following methodological practices and approaches: conceptual formalization, comparative historical analysis, comparative political science analysis, multivariate analysis, narrative analysis, political discourse analysis, conceptual analysis, system analysis, problem-chronological analysis, statistical presentation of data. Also convincing is the use of a multiparadigm approach and an appeal to such areas as political elitology, political communication studies, political realism and political pragmatism, institutionalism and neo-institutionalism.