The [1.1.1]propellane radical cation 1(•+), generated by radiolytic oxidation of the parent compound in argon and Freon matrices at low temperatures, undergoes a spontaneous rearrangement to form the distonic 1,1-dimethyleneallene (or 2-vinylideneallyl) radical cation 3(•+) consisting of an allyl radical substituted at the 2-position by a vinyl cation. In similar matrix studies, it is found that the isomeric dimethylenecyclopropane radical cation 2(•+) also rearranges to 3(•+). The unusual molecular and electronic structure of 3(•+) has been established by the results of ESR, UV-vis, and IR spectroscopic measurements in conjunction with detailed theoretical calculations. Also of particular interest is an NIR photoinduced reaction by which 3(•+) is cleanly converted to the vinylidenecyclopropane radical cation 4(•+), a process that can be represented in terms of a single electron transfer from the allyl radical to the vinyl cation followed by allyl cation cyclization. The specificity of this photochemical reaction provides additional strong chemical evidence for the structure of 3(•+). Theoretical calculations reveal the decisive role of vibronic coupling in shaping the potential energy surfaces on which the observed ring-opening reactions take place. Thus vibronic interaction in 1(•+) mixes the (2)A(1)' ground state, characterized by its "non-bonding" 3a(1)' SOMO, with the (2)E'' first excited state resulting in the destabilization of a lateral C-C bond and the initial formation of the methylenebicyclobutyl radical cation 5(•+). The further rearrangement of 5(•+) to 3(•+) occurs via 2(•+) and proceeds through two additional lateral C-C bond cleavages characterized by transition states of extremely low energy, thereby explaining the absence of identifiable intermediates along the reaction pathway. In these consecutive ring-opening rearrangements, the "non-bonding" bridgehead C-C bond in 1(•+) is conserved and ultimately transformed into a normal bond characterized by a shorter C-C bond length. This work provides strong support for the Heilbronner-Wiberg interpretation of the vibrational structure in the photoelectron spectrum of 1 in terms of vibronic coupling.