Joseph S. Nye jr. (Distinguished Service Professor at Harvard University, Kennedy School of Government) is supposed to be one of the best-known theorists in the political-scientific field of international relations. In June 2017 he visited Vienna for the first time, where he gave brilliant lecture on “American Geopolitics in the 21st Century” at the National Defence Academy. Nye had followed an invitation by the research group Polemology & Legal Ethics (Faculty of Law of the University of Vienna) in cooperation with the Directorate for Security Policy (MoD). In the essay at hand some relevant arguments of Joseph Nyes concerning this context are to be taken up, discussed polemologically (i.e. triadly in the sense of geo-politics/geo-economy/geo-culture), and, if sensible, contrasted against the assessments of other distinguished theorists of international relations. Geo-politics is defined according to the imperatives of global perceptions of order. As far as security policy is concerned, the world has “caught fire” for good in the 21st century at the latest. At the moment we witness global security-political challenges, from overflowing trans-national terrorism, erratic proliferation of nuclear weapons, alarming threats by so-called rogue states such as North Korea, to a massive climatic change as well as omnipresent threats in cyber space. The USA have generally abandoned their role as „benevolent hegemon”, have perceptibly retreated as a stabilising instance and/or “globocop”, and have consciously displaced their security-political interest regionally towards the Pacific. The vacuum in the geo-political system of power will be filled by that actor who has a prudent mix of kinds of power ready, both Hard Power and Soft Power. In the sense of Nyes, this is Smart Power, an intelligent kind of power where a political actor must understand, sometimes compensating, how to transform oftentimes limited resources into desired results. In the 21st century, power - particularly in the context of global politics, as a display of intransitive power - is much more based on a „power-to“ (Smart Power), i.e. the component of authorisation and of figuration, than on pure transitive dominance in the sense of “power-over” (Hard Power). The third level - „power with“ (Soft Power) - reflects the capability of developing strategies in mutual consent. Nevertheless, the unbroken effective potential of hard power can be deduced from any sound power-theoretical mental model by means of the antagonism carrot and stick. Often it is sufficient to merely threat with the stick, but here one requires serious threatening potential. The same holds true for smart power, which can also be the substrate of a power of data flows. The cyber-dimension of exerting power has increased in relevance as far as geopolitics is concerned. If a matrix-like linking of these schemes of power with the polemological key factors geo-politics, geo-economy and geo-culture is successful, a complete picture of geo-strategic power in the 21st century is the result of the composite view. Anyway, one can figure out precious assets from the substantial geo-power-political oeuvre of Joseph Nyes.