The X-ray and extreme ultraviolet spectra produced by solar wind ions undergoing change transfer collisions with the atoms and molecules present in the atmospheres of comets are calculated. The calculations take account of the cascading transitions that follow electron capture into highly excited states. It is shown that sequential collisions cause the X-ray spectrum from the cometary center to be softer than that of the peripheral regions. Some of the brightest lines arise from forbidden transitions of helium-like oxygen and carbon ions. The X-ray luminosities and averaged spectra reflect the composition of the solar wind. The calculated luminosities and spectra corresponding to a typical distribution of impinging solar wind ions are consistent with observations of comets Hyakutake and Hale-Bopp. The spectral resolution required to establish charge transfer as the source of cometary X rays is discussed; an energy resolution of 10 eV should be adequate. ¿ 2000 American Geophysical Union