Summary: A general synthesis method is developed for the dynamic analysis of nonconservative vibratory systems composed of substructures. The idea of the synthesis is to represent each substructure by a reduced-order model and to couple the substructure models together to act as the whole system. For general nonconservative systems, a state space formulation is adopted for each substructure. Reduced-order substructure models are obtained by approximating each state vector as a linear combination of a small number of real trial vectors. The accuracy with which the synthesized model represents the whole system depends on the choices of trial vectors and the number of vectors used. A procedure is developed for increasing the accuracy by iteratively generating improved substructure trial state vectors.