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The light-intensity fluctuations in each longitudinal mode of CW AlGaAs-GaAs stripe-geometry double-heterostructure junction lasers which oscillate in many modes are investigated experimentally, when the operating current is within a few tens of percent above threshold. In addition, experimental results about the noise characteristics for the lasers directly modulated are discussed in relation to the lasing-spectrum broadening. The total intensity output can be well stabilized at currents above threshold by larger than 10 percent, even when the same laser is modulated by large pulse currents at such high speeds as 400 Mbits. However, the relative noise power for each mode is about 30 dB larger than that for total modes within the whole frequency region observed in this work, and the noise spectrum becomes essentially flat when the laser is modulated. The relative fluctuations for each mode of the modulated laser seems to be nearly equal to the low-frequency fluctuations in each mode without modulation for a given normalized pump rate.