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The use of current-modulated semiconductor lasers for optical heterodyne spectroscopy has been investigated at modulation frequencies up to 2.6 GHz. The current modulation produces a simultaneous frequency and amplitude modulation of the laser output. A characteristic heterodyne spectrum occurs when the modulated laser probes a narrow absorption line. In order to analyze the measured spectra, a complete line shape theory has been derived for heterodyne spectroscopy with frequency- and amplitude-modulated laser light. The results show how the obtained signals depend on the modulation frequency and the phase difference between the frequency and the amplitude modulation. The measurement technique permits investigation of the FM-AM phase difference of current-modulated semiconductor lasers.