Compound systems composed of two or more substructural systems are studied in this project. Relative motions exsit among the substructural systems, which are mainly in stochastic manner. Random vibration is the significant character of these compound systems. This is a fundamental problem in various practical engineering fields, which has applications to structures such as trains and railroad tracks or railroad bridges; vehichles and highway bridges, parking grages and aircraft carriers, advanced propulsion concepts such as railguns, high speed precision machining, etc. The dynamic responses among multiple substructures are coupled one another during high speed relative motions and behave in strong non-stationary maner. Up to now, it has no general methods to deal with this complicated problom. In this project, a general modal synthetical method based on the hybrid energy and hybrid variable method will be firstly established, and the three-dimensional stochastic dynamic model of compound systems will be proposed. General solution procedures will be developed for the coupled stochastic dynamic equation of compound sstructural systems, which can efficiently deal with the non-stationary coupled action among substructural systems. It is essentially for practical application and the development of random vibration theory.