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We perform modal analysis of short-term swing dynamics in multi-machine power systems. The analysis is based on the so-called Koopman operator, a linear, infinite-dimensional operator that is defined for any nonlinear dynamical system and captures full information of the system. Modes derived through spectral analysis of the Koopman operator, called Koopman modes, provide a nonlinear extension of linear oscillatory modes. Computation of the Koopman modes extracts single-frequency, spatial modes embedded in non-stationary data of short-term, nonlinear swing dynamics, and it provides a novel technique for identification of coherent swings and machines.