  A specific model of parity-conserving lepton substructure is considered. We
show that a positive-definite contribution to the muon $(g-2)/2$ at the
possible level of about $4\times 10^{-9}$, can be related to a significant
increase in the interaction cross section for cosmic-ray neutrinos with
energies above about $10^{19}$ eV. The additional cross section at $\sim
10^{20}$ eV is calculated to be $\sim 10^{-29}$ cm$^2$, which is about 100
times the standard weak-interaction cross section. The model involves an
extremely massive, neutral lepton, with $m_L\cong 2\times 10^6$ GeV fixed by
the new contribution to $(g-2)/2$.
