At low temperatures the linewidths in the electron resonance spectrum of manganous ions dissolved in methanol exhibit an unexpected and unusual dependence on the nuclear quantum number. The dominant relaxation process is still modulation of the zero-field splitting, as at higher temperatures. However, the mixing of the spin states by the non-secular hyperfine terms in the static spin hamiltonian is now important, and is responsible for the dependence of the linewidth on the nuclear quantum number.