Density functional calculations are presented on the structure and magnetic parameters of the perfluorinated ethyl and n-propyl radicals and compared with the non-fluorinated analogs. It is found that fluorine substitution leads not only to nonplanarity at the radical center but to delocalization of spin density onto the F-alpha atoms and to spin polarization effects that both lead to pronounced anomalies in the anisotropic contribution to the hyperfine tensor. The nonplanar radicals do not obey the traditional McConnell relations. They serve as model systems for similar species that are observed in perfluorinated polymers.