Existing methods for testing the global identifiability of linear dynamic systems depend upon algebraic manipulation of nonlinear equations; this is a manual task not amenable to computerisation and one where the work effort tends to be prohibitive for systems with more than three states-A major breakthrough is reported based upon a novel variant of normal-mode analysis. The method begins with bilinear equations and reduces these by stages according to well-defined rules into subsets of independent linear equations. The effects on identifiability of changes in model structure are immediately apparent, which makes the procedure valuable for computer-aided design of optimum experimental conditions. The decomposition procedures are demonstrated via numerical examples, including application examples from chemical reaction kinetics and mineral ore processing.