The author illustrates the key issues of processes of the FR Yugoslavia (Serbia and Montenegro) before the International Court of Justice in The Hague (ICJ). Focused on explanations for the ICJ determination of the legal foundations for jurisdiction in accordance with international law, he gives legal remarks on reasons why the ICJ was able to consider them in the case of the Bosnia and Herzegovina vs. FR Yugoslavia (Serbia and Montenegro) and why it decided to lack jurisdiction in the cases against NATO. Examinations of the legal facts of the state responsibility do not prejudge questions of the jurisdiction of the ICJ that should be open in the case between Croatia and Serbia and Montenegro. The author's remarks follow the preliminary procedure of the ICJ and help consider the real state of all instituted proceedings.