Metalloradical species [Co2 Fv(CO)4 ](.+) (1(.+) , Fv=fulvalenediyl) and [Co2 Cp2 (CO)4 ](.+) (2(.+) , Cp=η(5) -C5 H5 ), formed by one-electron oxidations of piano-stool cobalt carbonyl complexes, can be stabilized with weakly coordinating polyfluoroaluminate anions in the solid state. They feature a supported and an unsupported (i.e. unbridged) cobalt-cobalt three-electron σ bond, respectively, each with a formal bond order of 0.5 (hemi-bond). When Cp is replaced by bulkier Cp* (Cp*=η(5) -C5 Me5 ), an interchange between an unsupported radical [Co2 Cp*2 (CO)4 ](.+) (anti-3(.+) ) and a supported radical [Co2 Cp*2 (μ-CO)2 (CO)2 ](.+) (trans-3(.+) ) is observed in solution, which cocrystallize and exist in the crystal phase. 2(.+) and anti-3(.+) are the first stable thus isolable examples that feature an unsupported metal-metal hemi-bond, and the coexistence of anti-3(.+) and trans-3(.+) in one crystal is unprecedented in the field of dinuclear metalloradical chemistry. The work suggests that more stable metalloradicals of metal-metal hemi-bonds may be accessible by using metal carbonyls together with large and weakly coordinating polyfluoroaluminate anions.