Introduction. The dynamic interaction features in mechanical oscillating systems, whose structure includes additional couplings, are considered. In practice, such cases occur when using various optional mechanisms and motion translation devices under the formation of technical objects. The study objective is to develop a method for constructing mathematical models in the problems of dynamics of the mechanical oscillating systems with optional devices and features in the system of external

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... bing factors.Materials and Methods. The techniques used to study properties of the systems and the dynamic effects are based on the ideas of structural mathematical modeling. It is believed that the mechanical oscillating system, considered as a design model of a technical object, can be compared to the dynamically equivalent automatic control system. The mathematical apparatus of the automatic control theory is used.Research Results. A method for constructing mathematical models is developed. The essential analytical relations for plotting oscillating systems are obtained, which enable to form a methodological basis for the integral estimation and comparative analysis of the initial system properties in various dynamic states. Dynamic properties of the two-degree-offreedom systems within the framework of the computer simulation are investigated. The implementability of dynamic oscillation damping mode simultaneously in two coordinates with the joint action of two in-phase kinematic perturbations in the mechanical oscillating systems is shown.Discussion and Conclusions. The possibilities of new dynamic effects, which are associated with the change in the system structure under certain forms of dynamic interactions, are noted. The study is of interest to experts in machine dynamics, robotics, mechatronics, nano and mesomechanics.