In this paper I argue that there are huge differences in the concepts of cyberwar in Russian and American politico-military thought. Cyberwar is a part of modern hybrid war. In the American views, the latter was coined to describe certain new forms of warfare, above all in the Middle East. It is based on analysis of the experience of various terrorist and jihadist groupings acting in the area. In the Russian tradition, before the disintegration of USSR “hybrid war” (although different terms were used) referred rather to political and information operations. In this century, the Russian concept was developed in a close relation with coloured revolutions, the Arab spring, the Russian intervention in Ukraine and the perception that the country is permanently attacked by the US and their Euro-Atlantic allies. Here, the Russian and the US concepts are compared by origin, conceptual basis, scope, nature, time to be waged, tools, relations with other fields, how are they organized and who are the cyber actors. Fundamental differences are established, and this is one of the reasons for certain ineffectiveness of the West in meeting the challenges of modern Russian hybrid war in general and cyberwar in particular.