A new semi-analytical framework for the study of passive or active engine mounting systems is presented. It recognizes that most practical problems incorporate a nonlinear mount or isolation element and the resulting physical system, consisting of the engine, mount and flexible base, involves many degrees of freedom. Unlike linear systems, sinusoidal excitation produces a periodic response, including super- and sub- harmonics. Two example case systems are employed to illustrate key concepts of the framework. The first numerical example case involves a passive hydraulic engine mount with an inertia track. The second example case is a novel experimental system that has been developed to study active and passive, nonlinear mounting problems. New analytical and experimental results are presented and various nonlinear phenomena are considered. The impact of nonlinearity on vibratory power transmission and active control is also investigated. Further development of the proposed framework is expected to yield an efficient and useful tool for the analysis of passive, semi-active and active mounts for engines and other comparable machines.