The article deals with Donald Trump’s ascent to the White House that may open a new phase in the international relations, and foremost in relations between Russia and the USA. This is determined by the very Trump phenomenon, which is neither accidental, nor confined exclusively to the American politics, but reflects deep changes in the life of many nations and world environment as a whole. Donald Trump is a product of the world’s anti-globalist trend – populism. That is why he remains for the time being one of the most unpredictable politicians. Russian leadership obviously gave preference to Trump during the US election campaign. The main reason of such attitude of the Russian elite towards Trump was his political line of rejecting foreign policy of President Barak Obama, under whom Russian-American relations sank to the lowest point since the end of the Cold War. In order to estimate the possibility of substantial improvement under Trump it is worthwhile once again to address the reasons of the crisis of the recent few years in the relations between the two powers with the purpose of understanding how probable the removal of these reasons in the future. In view of the domestic political situation in the USA and spontaneous nature of Trump’s pre-election declarations, it is still not clear which policy course will be implemented by his administration, if and when it elaborates a consistent foreign policy. This is not the whole present uncertainty, however. No less unpredictable are the changes in Russian policy in reaction to what is happening within the United States and if the changes happen – which direction they will take. Moreover, in the situation of domestic political chaos and actual paralysis of state authority in the United States, the future of the relations between the two powers depends presently more on Russia, its ability to quickly adapt to the changing situation and come out with big, concrete initiatives aimed at directing its dynamics to a constructive channel.