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This paper develops a measurement-based method for estimating a two-machine reduced model to represent the interarea dynamics of a radial, multimachine power system. The method uses synchronized bus voltage phasor measurements at two buses and the line current on the power transfer path. The innovation is the application of the interarea oscillation components in the voltage variables resulting from disturbances for extrapolating system impedances and inertias beyond the measured buses. Expressions for the amplitudes of the bus voltage and bus frequency oscillations as functions of the location on the transmission path are derived from a small-signal perturbation approach. The reduced model provides approximate response to disturbances on the transfer path and offers an alternative to model reduction techniques based on detailed system models and data.