The hyperfine (hf) structures of radical cations are calculated using first principles density functional theory. Within the local spin density (LSD) approximation, the isotropic hyperfine coupling constants (Fermi contact terms) are computed for a set of linear (nonbranched) alkane and alkene radical cations with up to four carbon atoms. The results are as a whole in very good agreement with experimental data, obtained from low temperature matrix isolation electron-spin resonance (ESR) measurements, and with results from previous configuration interaction calculations.