The space applications of composites obtained by dispersing carbon nanotubes within high-density polyethylene are analyzed. Electron spin resonance investigations on proton-irradiated composites are reported. The effect of ionizing radiation of the parameters of electron spin resonance spectra is studied. A radiation-induced increase of the concentration of uncoupled electronic spins delocalized over the conducting domains of carbon nanotubes is reported. It is concluded that radiation-induced modifications in such composites are weak.