The power spectra of the wideband (10 Hz to 100 kHz) magnetic field signals in a number of lightning return strokes (primarily first return strokes) measured during a lightning storm which occurred in Lindau in August 1984 have been calculated. The RF magnetic field data were obtained with the engineering unit of the Galileo Jupiter Probe lightning experiment. In the analysis, each return stroke data set is first passed through an adaptive filter designed to whiten its spectrum. The largest sample in the filtered output is set to zero, and the power spectrum of the filtered data stream is computed using five orthogonal prolate spheroidal data windows in the time domain and a fast Fourier transform algorithm. The spectra of the magnetic field data defintely show fine structure, with two or three distinct peaks appearing in the spectra of many of the waveforms. An enhancement of power at f ~60--70 kHz is often seen in the spectra of the waveform time segments preceeding and following the rise-to-peak amplitude of the return stroke. ¿ American Geophysical Union 1989