Single-mode (SM) laser radiation from a GaAs diode is obtained using a composite cavity which can be tuned to select a desired spectral mode. The properties of a laser with such a cavity are described. The kinetics of the spectra of the single-mode strip double-heterostructure laser is investigated with a high time resolution (10-10s) spectrometer apparatus. At sufficiently high currents above threshold a transition from SM to multimode operation occurs with breaks in the stable SM oscillation. Such an event is accompanied by a frequency self-modulation of the oscillation with a self-induced intensity pulsation at the same microwave frequency. Multimode oscillation appears simultaneously with the pulsation of the radiation, and the SM output power is limited due to such pulsations.