The subject. The qualification’s problem of a crime jointly committed by two or more people, only one of whom is criminally liable, is ambiguously resolved. It is shown that there is a case law tendency to bring into the scope of criminal liability all of people, who have participated in committing a crime together, as accomplices and co-perpetrators. However, it does not correspond to the main theory of complicity, according to which a group of perpetrators being a form of complicity consists exclusively of criminally liable offenders. And, moreover, there is a plenty of sentences, in which courts confirm that a criminally unliaible person is not able to be one of accomplices and co-perpetrators, as a consequence another offender is individually responsible for committing a crime.The goal of the study is to determine whether joint commission of a crime by two or more people, only one of whom is criminally liable, constitutes complicity and a group of perpetrators. General (analysis, synthesis) and private scientific (formal-dogmatic, historical-legal) methods are used to achieve the goal.The main results. In case law qualification of joint commission of a crime by two or more people, only one of whom is criminally liable, has gone through several stages in its development and directly depended on a type of the crime. Regional case law often does not coincide with the position of the Supreme Court of the Russian Federation. There are three main theories in criminal law science, according to which joint commission of a crime by some people, only one of whom is criminally liable: (a) forms both complicity and a group; (b) does not form either complicity or a group; (c) forms a group without signs of complicity.Conclusion. Joint commission of a crime by two or more people, only one of whom is criminally liable, constitutes a group of perpetrators without signs of complicity. The interpretation dividing complicity and a group of perpetrators into two different institutions allows to take into account a group way of committing a crime as a feature of the objective side and define criminally liable offenders.