The end of the XX-th century was marked by dramatic changes on the geopolitical ground, which was generated, first of all, by the USSR collapse. Political confrontations that accompanied the process of USSR collapse caused in early 90-es violent conflicts at the periphery of the former soviet empire (in the Republic of Moldova, for example). The path pursued by the Republic of Moldova from 1992-2003 to settle its conflict was reduced to negotiations with the Transdniestrian separatist administration and signing of a great number of documents with the participation of the Russian Federation, Ukraine and Organization for Security and Cooperation in Europe (OSCE). After some events (for example, refusal of signing “Kozak Memorandum”) the negotiation format was changed. In the process were involved two new negotiators representatives of USA and European Union, which have expressed their own positions and interests, provided new visions and aspects. The Transnistrian conflict reached the international level and actually is discussed in the framework of Council of Europe, European Commission and other international organisms, which represent an significant importance in the politics of solution of the conflict. The specialists of different states and domains elaborate some ways and variants to solve one of the conflicts of the post-soviet space.