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We present a derivation of the noise spectra of multielement semiconductor lasers. We model the noise by a set of Langevin sources which drive a system of small-signal field equations. The Langevin sources are normalized to transition rates within the laser and general formulas for relative intensity, frequency fluctuation, and field spectra are produced. We evaluate the formulas for several specific cases of interest, including those of a passive-active resonator and active-active coupled cavity resonator. In each case, the linewidth is governed by effective α-parameter(s) which generally differ from the material parameter. In the active-active cavity, the linewidth consists of two parts, one which is similar to the Schawlow-Townes linewidth, and a second which is proportional to the FM modulation index.