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Frequency response and eigenvalue techniques are fundamental tools in the analysis of small signal stability of multimachine power systems. This paper describes two highly efficient algorithms which are expected to enhance the practical application of these techniques. One algorithm calculates exact eigenvalues and eigenvectors for a large power system, while the other produces the frequency response of the transfer functions between any two variables in the system. This paper also presents alternative computing procedures for the AESOPS eigenvalue estimation algorithm which are simpler and at least as efficient as those described in .