In this paper the basic methodology of the coupled response-degradation modelling of stochastic dynamical systems is presented

along with the effective analysis of selected problems. First, the general formulation of the problems of stochastic dynamics coupled with the evolution of deterioration process is given. Then some specific degrading oscillatory systems under random excitation are analyzed with a special attention on the systems with fatigue-induced stiffness degradation. Both, the general discussion and the analysis of selected exemplary problems indicate how the reliability of deteriorating stochastic dynamical systems can be assessed.