Calculations of X ray spectra due to bremsstrahlung from precipitating auroral electrons at Jupiter and Saturn are presented. The model assumes that a field-aligned potential drop accelerates a primary beam of electrons into the atmosphere where a population of secondary electrons having a power law energy dependence is generated. The spectrum at Jupiter is normalized to the soft X ray observations of Metzger et al. (1983) at the low-energy end and constrained at the high-energy end by UV auroral energy requirements. The spectrum at Saturn is constructed by analogy to the Jovian case allowing for variation of the beam energy, energy flux, and scale size of the Saturnian aurora. The results indicate that a significant flux of X rays is emanating from both planets wich may serve as a basis for conducting planetary X ray astronomy as a part of future spacecraft missions to the planets. ¿ American Geophysical Union 1990