A scientific and methodological base is being developed in the direction of systems analysis and systems theory as applied to the problems of assessing the dynamic states of technical objects, the design schemes of which are represented by mechanical oscillatory systems with one or more degrees of freedom. Within the framework of the proposed approach, a mechanical oscillatory system is compared with a dynamically equivalent structural diagram of an automatic control system. Based on the concepts of objects, whose dynamic properties are estimated, on the external force and kinematic influences, typical elementary links, negative feedbacks, transfer functions and dynamic modes of mechanical oscillatory systems, a new technique is proposed, taking into account the motion transformation devices. On the basis of the developed approach there are obtained the new data on the dynamic properties of systems that include links with reduced elastic characteristics. The possibilities of creating a number of new dynamic effects in mechanical oscillatory systems reflecting the specificity of the vibration interaction of the elements of oscillatory structures are considered