Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Theoretical Foundations of the Organization of Banches and Repetitions in Programs in the Logical Programming Language Prolog D.V. ZDOR A program for any computer system is designed to process data. At the same time, dynamic data structures are used to process large amounts of data. The most commonly used dynamic data structures are lists. The need to use lists, on the one hand, and the absence of special operators for list processing in Prolog programs, on the other hand, actualizes the problem of finding the theoretical foundations for solving list processing problems. The use of recursion is a tool for solving list processing problems in Prolog. The purpose of the work is to analyze the execution of recursive rules for processing lists. Analysis of special literature on the topic of research, generalization and systematization of knowledge, testing of the program, analysis of the progress of the program. The construction of solving problems for processing lists in a program in the Prolog language is considered. A detailed analysis of the execution of recursive predicates in list processing tasks is carried out. The design features of the recursive rule and the conditions for terminating the recursion depend on the type of the list processing problem being solved. Using the example of the problem of checking whether an element belongs to a list, the article describes in detail the mechanism of using recursive rules at the level of matching predicates and instantiating variables in the context of solving problems of processing lists. The given example can serve as a technological basis for solving other problems of processing lists. The results obtained can be used in the further development of the issues of using recursive predicates in problems of list processing, as well as used in the educational process when studying the theoretical foundations of computer science and logical programming in the Prolog language. Keywords: dynamic data structure, list, recursive rule, recursion termination condition. DOI: 10.25791/pribor.5.2021.1258 Pp. 17-21.