The article deals with problematic issues arising in the activities of the preliminary investigation bodies related to the implementation and completion of criminal investigations in the absence of a suspect, accused at the place of investigation and the impossibility of conducting investigative and procedural actions during his absence. Difficulties arise when declaring a wanted person and organizing the establishment of his location. Often, persons hiding from the preliminary investigation, especially those undergoing criminal cases related to the commission of economic crimes, have financial opportunities and change their place of residence in order to avoid criminal liability and the application of penalties. When these persons are put on the wanted list, the problem of choosing a preventive measure in the form of detention also arises in the activities of the investigative bodies. Despite the fact that some of the wanted persons are accused of committing serious and especially serious crimes, a preventive measure has been chosen against them that is not related to detention. The problems considered in this article and the proposed solutions to them are a recommendation for persons whose official duties include searching for persons who have disappeared from the bodies of inquiry, investigation and court. Depending on the current operational or investigative situation, the algorithms of actions of law enforcement officers may change and be optimized.