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We derive a novel rate equation system for a laser consisting of two coupled cavities arranged in tandem. The derivation of the photon rate equations is based on classical electromagnetic theory, while the rate equations for the electrons are written down heuristically in analog with the conventional laser rate equations. This paper discusses the initial numerical evaluation of our coupled-cavity laser model which indicates that the laser tends to oscillate more readily in a single longitudinal mode than a single-cavity laser of comparable length. The enhanced mode selectivity stems from the constructive and destructive interference of the fields in the two coupled cavities. Suppression of secondary longitudinal modes by more than 20 dB is readily obtainable. The coupled-cavity laser maintains single-wavelength operation even if the peak of the gain profile shifts over a certain wavelength range. However, when it finally responds to a sufficiently large shift of the gain profile, it does so by jumping discontinuously to a new (single) operating wavelength. Further investigations of frequency tuning by means of the injection current as well as studies of the frequency instability due to temperature and refractive index variations will be reported in a separate publication.