We show that a periodic metal-metal multilayer nanostructure can serve as an efficient source of hard x-ray transition radiation. Our research effort is aimed at developing an x-ray source for medical applications, which is based on using low-energy relativistic electrons. The approach toward choosing radiator-spacer couples for the generation of hard x-ray resonant transition radiation by few-MeV electrons traversing solid multilayer structures for the energies of interest to medicine (30–50keV) changes dramatically compared with that for soft x-ray radiation. We show that one of the main factors in achieving the required resonant line is the absence of the contrast of the refractive indices between the spacer and the radiator at the far wings of the radiation line; for that purpose, the optimal spacer, as a rule, should have a higher atomic number than the radiator. Having experimental goals in mind, we have considered also the unwanted effects due to bremsstrahlung radiation, absorption and scattering of radiated photons, detector-related issues, and inhibited coherence of transition radiation due to random deviation of spacing between the layers. Choosing as a model example a Mo–Ag radiator-spacer pair of materials, we demonstrate that the x-ray transition radiation line can be well resolved with the use of spatial and frequency filtering.