A generalised approach to modelling multimachine systems is presented for stability analysis. The more systematic and realistic representation, accompanied by the development of powerful eigenvalue-analysis techniques, facilitates the study of the oscillation behaviour of complex interconnected systems, The study highlights the dependence of instability tendencies on large power angle differences between machines and incompatible excitation characteristics for the various machines. Based on this understanding, alternative practical remedies are investigated. The analytical approach developed, together with the discussions in the paper, also provides a firm basis for considering the introduction of PSSs into multimachine systems. Application of the modal and sensitivity methods to PSS study is described in a companion paper.