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A practical digital computer method for obtaining eigenvalue sensitivities of interconnected power systems is presented. The method is especially suited to the analysis of detailed modelled synchronous machine systems where shaft and stator-network dynamic effects are significant. A unified structure in the construction of the state space equations permits the inclusion of a wide variety of control equipment and varying degrees of modelling complexity. Sample results are given for typical cases illustrating the significance of eigenvalue sensitivities. Specifically results are presented for a 4 generator hydroelectric system and for a 2 generator system exibiting subsynchronous torsional resonance.