We determine a stationary measure for a process defined by a differential equation with phase space on the segment [ V 0 , V 1 ] and constant values of a vector field that depend on a controlling semi-Markov process with finite set of states.In problems of reliability, in the course of the determination of stationary indices of efficiency and reliability of systems, there arises the problem of finding stationary distributions of processes that simulate these systems [1 -3] (Secs. 3 and 4). For the investigation of multiphase systems with accumulators, stochastic processes of transfer with delaying screens in a Markov or semi-Markov medium are used as simulating objects [2,3]. In the case of a semi-Markov controlling process, one investigates the stationary distribution of the corresponding three-component Markov process whose first component is a time variable (the time passed from the moment of the last change in the state of the controlling process), the second component corresponds to the state of the controlling process, and the third component is the space variable that describes the fullness of accumulators. The problem of the determination of a stationary distribution in the semi-Markov case is nontrivial even in the simplest case of an alternating controlling process [3].In the present paper, we generalize the result obtained in [3] for a single-phase system to an arbitrary finite phase space of a controlling process in the case of balance.Consider the equationwhere κ ( t ) is a semi-Markov process with the phase space G = X ∪ Y, X = { x 1 , x 2 , … , x n }, Y = { y 1 , y 2 , … , y m }, the transition-probability matrix P = p G αβ α β , , ∈ { } , p αβ = P κ α κ l l + { = / 1 = β }, of a Markov chain k l , l ∈ N, imbedded into κ ( t ), and the sojourn time τ α in a state α ∈ G that has a general distribution function F α ( t ).It is known (see [5] (Chap. 3) and [6]) that Eq. (1) describes a stochastic process of transfer in a semi-Markov medium.Assume that the following condition is satisfied:(C 1 ) there exist the density f α ( t ) = d F t dt α ( ) and the moments