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Previous work on the resonant modes of GaAs junction lasers operating near threshold is extended to include spectra obtained at currents 1.5 to 3 times the threshold level. At these currents, two families of modes are shown to oscillate simultaneously with different center frequencies. The modal families are demonstrated to correspond to different mode numbers in the direction perpendicular to the junction plane. These observations are found to be in agreement with a previously reported theory for the GaAs laser cavity, which allows a dielectric constant variation in both directions transverse to the laser axis. The general characteristics of the observed spectra are explained qualitatively in terms of a derived mode dependence of the steady-state gain function. It is suggested that the strong frequency dependence of the spatial gain distribution perpendicular to the junction plane can allow two modal families with different mode numbers perpendicular to the junction to oscillate simultaneously with different center frequencies.