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The paper presents the findings of the investigation of initiation conditions for parametric resonances in the nonlinear system “Engine unit - Torque Converter - Planetary Transmission Elements (Drum and Lined Plate)”. The mentioned oscillations and resonances form dynamic loading of powertrain lined plates. In terms of the research results the paper validates the ways of tuning parametric oscillations. These ways provide for the increasing of durability of multiplate clutches plates of vehicle powertrain. The evaluation of dynamic stability was performed on the basis of the analysis of Mathieu equation and Ince-Strutt diagram. The restriction of modulation depth parameter is proposed by filtering of high-frequency disturbances which are generated in the nonlinear system by different oscillation sources (power unit - internal combustion engine (ICE) or electric motor (EM), hydrodynamic processes in the hydraulic transformer - torque converter or hydraulic coupling, oil supply pump).