In the article, the author emphasizes that the constant trend of recent decades in many countries of the world has become the creation of a normative basis for the maximum efficiency of criminal proceedings by regulating the forms of simplified proceedings, taking into account the severity of the criminal offense, the totality of the collected evidence and the behaviour of the accused, etc. It is noted that the material and legal criterion, which is the basis for differentiating the forms of pre-trial investigation and distinguishing inquiry, includes:
 1) the nature, type and degree of severity of the criminal offense; 2) the type of punishment that can be imposed for its commission. It is proposed to consider the inquiry as a simplified form of pretrial investigation, which is carried out in relation to criminal misdemeanours, characterized by greater speed and efficiency compared to pre-trial investigation, which is achieved due to the reduction of procedural terms, simplification of the procedural form and expansion of the system of procedural sources of evidence. Among the features of inquiry as a simplified form of pre-trial investigation in criminal proceedings, the following are highlighted: 1) procedural speed; 2) simplification of the procedural form; 3) greater efficiency compared to pre-trial investigation; 4) expanded system of procedural sources of evidence; 5) the possibility of further implementation of simplified court proceedings. Some historical aspects of the creation of a two-link system of criminal offenses in the national criminal legislation of Ukraine with their division into criminal misdemeanours and crimes are considered. Attention is drawn to the separate problems of normative regulation of pretrial investigation terms in the form of an inquiry, as well as to the actual judicial practice of the Supreme Court regarding their overcoming. Some signs and manifestations of the simplification of the criminal procedural form of inquiry are considered.