In the article the authoress analyzes the Convention on the Prevention and Punishment of the Crime of Genocide in the work of national courts. National courts are not willing to deliver interpretations of the elements of the crime of genocide. In this question the judgements are rather superficial if compared with international rulings concerning the genocide. With few exceptions the courts based on the practice of international courts. Few exceptions which can be mentioned are: the question of 'destruction of the group' in the case of Jorgic, and the broaden definition of the national group elaborated by the Spanish courts. Prosecutions for the genocide by national courts are only a few, and this practice had little to contribute to the elements of the crime of genocide. The courts neither interpret the notion in the new terms nor even add some new interpretations to the practice of tribunals ad hoc. Suprisingly that international tribunals developed tha law of genocide although the domestic courts should be the courts of the first resort, what naturally means also the first 'source' of interpretation.Another fact which is worthy of note - is that national courts prosecute genocide on the base of universal jurisdiction, Spanish and German courts stated that art. VI of the Convention does not prevent the exercising of the universal jurisdiction. Almost 50 years ago in the case of Eichmann the District court of Jerusalem stated that determination of territorial jurisdiction is a compulsory minimum. According to the court, universal jurisdiction derives from the basic nature of the crime of genocide as a crime of utmost gravity under international law. In the authoress' view national courts should follow this standard. But maybe the most important development of the international law is connected in general with the prosecution of the crime of genocide in national and international courts and also with the dynamic interpretation of the said convention. Sixty years after the death of its author, Rafael Lemkin, the convention turned out to be a lively mechanism with the timeless value, which can be implemented to the situations created by the modern history.