We are considering a reliability system consisting of two restorable elements. The behaviour (intensity of work or repair) of the elements depends on each other. Switching between operating mode and repair mode and vice versa may not occur instantly. The time of such switching is random but limited. Obviously, in reliability theory, all random times have absolutely continuous distribution. Here, they can be mixed. The random time of work and repair of elements is determined using intensi- ties (or hazard rate function). These intensities depend on the full state of the system, i.e. on the state (work, repair) of each element and on the time of the stay in this state. In the general case, the random process describing the behaviour of such a system is not regenerative. We have identified the conditions under which this process is ergodic. Also, the conditions under which the upper polynomial bound for the convergence rate of this process distribution to the limit distribution can be calculated are defined.