In spite of the fact that Russia is a country of capitalism’s Jurassic Park and oligarchic capitalism, it has manifested itself as a geopolitical opposition to NATO, which raises a number of urgent and important questions and challenges to the Left: 1) NATO is world policeman. Will be Russia another world policeman? 2) New Cold War inevitable? 3) Do we need new world wide peace movement? Who can be main actors of this movement?