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We present a theoretical analysis of the lateral modes of a broad-area semiconductor laser. The structure of the modes are classified into four categories and the modes are traced in the frequency versus pump rate diagram. It is shown how the branches of the frequency tuning curves for the different types of modes are interconnected and how the intensity profiles develop along the branches. The main result of the paper is the presentation of a small-signal stability analysis which identifies the saddle-node and Hopf bifurcation points on the mode tuning curves. For stable modes we derive expressions for small-signal noise and modulation spectra and present numerical examples of the spectra.