Conformationally selective rearrangement of 1,1'-bicyclobutyl radical cations to radical cations of bicyclo[3.3.0]octane and bicyclo[3.2.1]octane that occurs at 77 K via the concerted one-step mechanism in a 1% 1,1'-bicyclobutyl solution in Freon-113 irradiated with X-rays at 77 K has been detected by means of the EPR technique. The assignment of the EPR spectra has been confirmed by MNDO-UHF calculations.