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A multistage identification algorithm for dynamic power system load models is proposed in this paper. The multistage approach is used to address the nonconvexity of the identification problem. Initial stages are used to find good preliminary estimates for the parameters of the model. Specifically, the initial stages are as follows: Equations for dynamic power system loads are discretized using the zero-order hold method and then approximated with a 2nd-order polynomial NARMAX model. Finally, an extended least squares approach is used to estimate the parameters of the NARMAX model, from which initial estimates for the parameters of the original model are obtained. In the final stage, the values found in the initial stages are used as the starting point for a Levenberg-Marquardt optimization routine that computes the optimal parameters. Numerical experiments using data from both simulated and real systems illustrate the computational complexity and accuracy of the proposed algorithm. Curve-fitting experiments are used to justify the polynomial NARMAX approximation.