The article is devoted to the peculiarities of the interrogation of a suspect (accused) in criminal cases of terrorist and extremist orientation. Interrogation is one of the most difficult investigative actions in tactical terms. The investigator or another person who takes testimony from the interrogated has to face a number of difficulties. The article highlights the problematic aspects of interrogation in a conflict situation of both procedural and tactical nature. Forensically, investigative tactics are based on scientifically proved recommendations from various fields of knowledge. The key in the verbal contact of the subjects of interrogation is knowledge from the field of psychology based on the characterological features of the criminal’s personality. The problem of identifying the psychological personality type of the interrogated person is associated with his various behavioral reactions to stimuli, as well as features of world perception, cultural, aesthetic preferences. The article defines the investigative task of recognizing the radical personality of the suspect (accused) to establish psychological contact with him (paranoid, hysteroid, epileptoid, emotive, hyperthymic, anxious and schizoid). Most of the considered tactics and combinations relate to the psychology of the relations of the opposing participants in criminal proceedings. On the one hand, this is an investigator, who must take truthful testimony and, on the other hand, a suspect (accused) who is trying to avoid criminal liability for an illegal act committed or minimize this liability. Tactical interrogation techniques developed in domestic criminology have been clarified by the author of the article and supplemented for the purposes of effective investigation of terrorism and extremism. The proposed recommendations for obtaining testimony can be used not only at the stage of preliminary investigation of crimes, but also during the pre-investigation check.