The radical cation of-methane isolated in neon matrices exhibits highly unusual electron spin resonance (ESR) spectral features between 2.5 and 11 K. The anomaly has been clarified by invoking large amplitude tunneling motions of the hydrogens among several symmetrically equivalent Jahn-Teller distorted structures. The effect of the tunneling motions upon the ESR spectrum was investigated by an analysis scheme based upon permutation-inversion group theory. All the deuterium substituted cations, i.e., CDH3+, CD2H2+, CD3H+, and CD4+ were also studied. The hyperfine coupling constant of C-13 was obtained from the study of (CDH3+)-C-13 and (CH4+)-C-13. Several independent generation methods were employed during the course of these methane cation studies, including photoionization, electron bombardment, x-irradiation, and a pulsed laser surface ionization technique.