The results of expert research in the field of forensic anthropology and forensic archeology help solve many important tasks: identify bone remains, determine the antiquity of a crime and can help historians and archaeologists find answers about the way of life, habits and level of civilization of a particular era. In some cases, even a historical investigation is possible, in which special knowledge of forensic anthropology and archeology can also come in handy. The study of skeletons and corpses, mummified remains of ancient people, cooperation with criminologists and historians helps not only to recognize certain individuals in the presence of materials for comparative research, but also to verify or refute more global versions of certain facts of the life of the entire historical society. The active development of forensic archeology and anthropology abroad provides a worthy example for domestic science and practice to borrow the positive experience of European and American colleagues. We see the use of the results of forensic archeology and forensic anthropology as part of a complex forensic investigation within the framework of the investigation of many offenses, in particular, illegal search operations at an archaeological heritage site, destruction, destruction or damage to cultural heritage sites. General scientific methods of research are empirical (experiment, observation, description) and theoretical (analysis, synthesis, abstraction, generalization, induction, deduction, explanation, classification, etc.), as well as systemic, functional, specifically sociological. The purpose of the article is to develop and analyze the theoretical foundations of conducting a complex forensic-medical and forensic-archaeological/forensic-anthropological examination during the investigation of illegal search operations at an archaeological heritage site, destruction, destruction or damage of cultural heritage sites and other offenses. First of all, when investigating the illegal conduct of search works at an archaeological heritage site, it is necessary to use the achievements of many sciences, to come to a systematic perception of the research object, to look for new interdisciplinary approaches. Secondly, when studying skeletonized remains and corpses, it is necessary to combine knowledge from forensic medicine, history, archeology and anthropology. It is necessary to develop a plan for the investigation of crimes taking into account the appointment of such types of examinations, to calculate certain deadlines and the complexity of investigations of this kind. Thirdly, to develop and test the methodology of conducting comprehensive forensic-medical and forensic-archaeological/forensic-anthropological examinations taking into account the achievements of these fields of knowledge and modern domestic technical and personnel capabilities. Fourth, to study the experience of foreign colleagues, in particular, American research centers and criminal proceedings, to improve the qualifications of certain specialists directly on international practice bases.