Abstract: The object of this research is RQ-systems (retrial queueing systems, systems with repeated calls) with the simplest incoming flow of requirements, waiting in orbit, return of requests and functioning in a random (semi-Markov) environment. The systems in question are models of a wide class of real service systems in which an application, upon completion of a successful service, can leave the system permanently or, after a certain period of time, return to the system for repeated maintenance. Examples of such systems are banks, where a customer who has repaid a loan can reapply for a new loan, employment centers, where customers can reapply in search of new work, etc. The efficiency of such systems depends on a number of factors, the nature of which can be defined as random (random semi-Markov environment). In this article, the author presents a mathematical modeling of the class of systems under study. The research tool of the systems under consideration is the mathematical apparatus of the theory of mass service. The proposed mathematical model of RQ-systems with the return of applications in a semi-Markov medium is investigated by the method of asymptotic analysis of markovized systems. The scientific novelty of the work lies in the fact that for the first time a mathematical model of an RQ-system functioning in a semi-Markovian environment with called applications was proposed and its asymptotic analysis was performed. The asymptotic average of the normalized number of customers in the system, the deviation from the average is found, the main probability-time characteristic is obtained - the probability density distribution of the values of the process of changing the system states.