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The development of a class of efficient numerical integration schemes for computing power system dynamic response is presented. These schemes are derived by making detailed use of the structural properties of the differential-algebraic system representation of the multimachine power system. The nonlinear differential-algebraic system is split into a nonstiff part with long time constants coupled to a stiff part with a sparse Jacobian matrix whose longest time constant is shorter than that of the first part. These two parts are linear in their respective states, i.e. the system is semilinear. With the nonstiff part removed, a smaller set of stiff equations with a smaller conditioning number than the original system is obtained. Consequently, longer stepsizes can be used so as to reduce the computation time. The proposed multistep integration schemes exploit the sparsity, stiffness and semilinearity properties. Numerical results indicate that these schemes operate with good accuracy at stepsizes as large as 100 times those necessary to ensure numerical stability for conventional schemes.