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A new method for investigating the spatial and temporal stability of semiconductor lasers is presented, which represents the first application of Hopf bifurcation theory to semiconductor lasers. Unlike the classical Hurwitz approach, whose applicability is restricted to a small number of piecewise homogeneous regions at most, details of the spatial distributions of carrier and photon densities can now be included with modest additional computational effort. The actual stability analysis involves solving no more than a 5 × 5 real eigenvalue problem once the steady-state distributions are known. This feature is particularly important where spatial variations play a fundamental role, Numerical results are presented to illustrate the application of the algorithm to oscillations and to nonlinear light-current characteristics in standard stripe-geometry lasers. The further application of the technique to the analysis of optical bistability and high-speed optical switching is discussed.