The condition monitoring (CM) of heavy-duty mining and metallurgical machines working under non-stationary loading and cyclic (reversal) speed-changing conditions is always accompanied by transient vibrations [1-3]. The presence of impulsive impacts results in false alarms, which cause either downtime for revisions or unexpected failures and significant production losses. The spatial and torsional vibrations of high amplitude have also resulted from the excessive linear, and angular backlashes, which should be considered as the main parameters for CM since most local defects in gears and bearings are following the dynamic overloads. However, the standard approaches are only partly suitable for backlashes diagnostics and predictive maintenance of such a class of machines. For example, triggering of recording beyond the transients and “angular” approach, i.e. data analysis synchronously with shaft revolutions, are somewhat challenging to implement in machines with a complicated structure. Some methods are developed for backlashes estimation in the automotive powertrains [4] and rolling mills [5] using transient vibrations. By representing the heavy gearboxes and shafts as multibody systems [6] with non-smooth stiffness characteristics [7] the diagnostics of bearings wear and bolted joints looseness can be efficiently conducted. In general, modal analysis is a proven method for diagnostics of damages in structures [8,9]. Such features of non-linear vibrations as nonisochronism, delay, the relation of dynamic response and static loads and damping factor can be used for diagnostic purposes. Examples of such machines where this approach is applied are steel rolling mills [10], load-haul-dump vehicles [11] and vibrating machines. Such difficult for diagnostics elements of vibrating screens as supporting springs and bolted joints on sieving decks can be diagnosed based on modal analysis using excitation from external periodical forces of inertial vibrators and stochastic impacts from the pieces of bulk material [12]. The diagnostics based on multi-body dynamical models can be conducted both on time series and in the frequency domain with different metrics (health indicators) derived from the transient signals analysis at the natural modes. The responses calculated on the dynamical models with linear parameters are used as the reference values in diagnosing non-stationary systems with piecewise linear stiffness. Statistical aspects of non-linear systems of machine loading are also important. It is shown that maximum dynamic load and its standard deviation in elastic couplings have a polynomial dependence on static input load. Based on conducted studies of different industrial machines, we actually propose a new strategy of predictive maintenance, which is characterized for a specific class of applications by the transition from monitoring of local defects to the monitoring of their causes – angular and radial backlashes, which is supported by the appropriate methods of their diagnostics. In addition, the verified models allow the accumulation in the computerized maintenance management systems (CMMS) of the fatigue cycles from dynamic loading in the critical elements of machines where measurement of torques and forces is unavailable [13]. The results of calculations on the multi-body models with non-linear stiffness characteristics are quite different from the FEM calculations conducted at the machine design stage when structural elements' deterioration is usually not included in the models. The analytical relations of the remain useful life (RUL) of elements with their degradation are shown in the examples.