This work focuses upon the grounds of declaring the applications against the former Soviet Union states either admissible or inadmissible by the European Court of Human Rights. Examining the Court admissibility decisions, it analyzes the procedural aspects of the system of human rights protection within the Council of Europe. It demonstrates that the procedural admissibility criteria are important especially with regard to new democracies and deserve more attention in order to achieve better effectiveness of the mechanism of human rights protection. This work reveals the grounds of inadmissibility common to the petitions against the Council of Europe relatively new member states. Identifying the frequently met inadmissibility grounds and suggesting correct understanding of admissibility criteria, it should be especially useful for the legal professionals working in the field of Human Rights Law, or anyone else who may be interested in the European Court of Human Rights.