Earlier studies have suggested the reliable estimation of the state of the rotor unbalance (both amplitude and phase) from a single run-down is a feasible procedure. Now a method has been proposed that can reliably estimate both the rotor unbalance and misalignment from measured vibration during a single machine run-down. Distinct, but related, approaches are presented for the case of flexibly and rigidly coupled rotor systems. The theoretical concept and the outline computational implementation used are presented in this paper. The method is demonstrated using experimental data from a machine with two journal bearings and a flexible coupling to the motor. A sensitivity analysis has also been carried out for the proposed method with perturbations to the rotor and fluid bearing models to confirm the robustness of the proposed method.