The paper considers the problem of the optimum preventive maintenance of the system with two elements and one re¬storing device. The system 's behaviour is described by a semi-Markov process with complex descrete and continuous set of states. Whether the preventive maintenance is performed depends on the state of the system's elements and the level of past life of the element which performs the duties of the main element. The paper contains the solution to the system of integral equations relative to the stationary distribution of a Markov chain included in given semi-Markov process. This results makes it possible to find various-stationary functionals on the process trajectories and lead the task of optimum control to searching the extreme value of given function of two real variables