The article researches the term “criminal influence” which was introduced to the Criminal Code of Ukraine (hereinafter – the CC of Ukraine) by the Law of Ukraine “On amendments to the Criminal Code of Ukraine regarding liability for crimes committed by criminal community”, and its correlation with the institute of complicity in a crime, in particular with objective elements of accomplices in a crime, as well as with illegal influence. The author concludes that there may be one narrow and two broad types of understanding of this term. Moreover, criminal influence may be considered not only from the criminal legal but also from the criminological point of view. Criminal influence is a part of the broader term of illegal influence. However, in contrast to other types of illegal influence, criminal influence, due to its social danger, is limited by the state specifically by the means of criminal law.The term of criminal influence introduced to the Ukrainian criminal legislation has serious gaps, so that it is extremely poor and practically inapplicable. Moreover, not only this term defined in the note to Art. 255 of the CC of Ukraine, but also corpus delicti provided for in Art. 255-1 of the CC of Ukraine (intentional establishment or dissemination of the criminal influence in society) should be substantially revised. The usage of general formulations and abstract concepts in the disposition of Art. 255-1 of the CC of Ukraine, as well as non-exhaustive lists of objective and subjective elements in the definition of the term of criminal influence violates the principle of legal certainty as a part of a broader rule of law principle. Bringing individuals to the criminal liability for committing crimes related to the criminal influence (intentional establishment or dissemination of the criminal influence in society and request for its application) or conviction of individuals for these crimes with a high probability will cause substantial violations of fundamental principles of criminal law and human rights.