Amorphous ferromagnetic ribbons are considered as a material for ferromagnetic cores for unresonant accelerating structures of 100...200-MeV ion accelerators. The manufacturing of the cores using this material are cheaper and easier than that of the cores made from common-used ferrites. Calculated and experimental characteristics of the ferromagnetic cores made from these ribbons (permeability and tangent loss) for a coaxial broad-band accelerating system are presented. These characteristics over the frequency range from 1 to 10 MHz are in good agreement taking into account the skin-effect. Possible versions of coaxial accelerating systems for medical synchrotrons with above mentioned cores are considered.