The article is devoted to the problem of nuclear non-proliferation and nuclear weapons reduction negotiations. Evaluation is made, to what extent nuclear states have performed their obligations under the first part of the Art.VI, the Nuclear Weapons Non-Proliferation Treaty (NPT). The author analyzes the influence of the Great Powers' policy aimed at nuclear arsenals curtailing and reduction of the nuclear weapons' role in national and international safety assurance, as well as at carrying of nuclear war concepts and plans far off stage in international military and political relations, at enhancement of the worldwide "taboo" against any use of nuclear weapons directly or as a threat, at lowering the popularity of nuclear weapons in inside politics of many countries.