It has been found difficult to explain both the absolute intensity and energy spectrum of the background component of cosmic X-rays in terms of a superposition of X-ray sources in distant galaxies [1] and of the inverse Compton collisions of metagalactic electrons with microwave photons [2]. Although the absolute intensity could be obtained by choosing suitable values of parameters which are not well known as yet, the gradual bending of the X-ray spectrum around 30 keV provides a critical test of theories. In this respect innerbremsstrahlung of intergalactic protons colliding with electrons is a candidate of background X-rays, since the X-ray spectrum is closely related to the proton spectrum and the latter usually bends in the non-relativistic region.