  In the Top-down scenarios, the decay of super-heavy particles
(m~10^{12-16}GeV), situated in dark-matter halos not very far from our Galaxy,
can explain the ultra-high-energy (UHE) cosmic-ray spectrum beyond the
Griesen-Zatasepin-Kuzmin cut-off. In the MSSM, a major component of the UHE
cosmic-ray flux at PeV-EeV energies could be given by the lightest neutralino
\chi, that is the lightest stable supersymmetric particle. Then, the signal of
UHE \chi's on earth might emerge over the interactions of a comparable neutrino
component. We compute the event rates for the resonant production of "right"
selectrons and "right" squarks in mSUGRA, when UHE neutralinos of energy larger
than 10^5 GeV scatter off electrons and quarks in an earth-based detector like
IceCube. When the resonant channel dominates in the total \chi-e,\chi-q
scattering cross section, the only model parameters affecting the corresponding
visible signal rates turn out to be the physical masses of the resonant
right-scalar and of the lightest neutralino. We compare the expected number of
supersymmetric events with the rates corresponding to the expected Glashow W
resonance and to the continuum UHE \nu-N scattering for realistic power-law
spectra. We find that the event rate in the leptonic selectron channel is
particularly promising, and can reach a few tens for a one-year exposure in
IceCube. Finally, we note that UHE neutralinos at much higher energies (up to
hundreds ZeV) may produce sneutrino resonances by scattering off relic
neutrinos in the Local Group hot dark halo. The consequent \tilde{\nu}-burst
into hadronic final states could mimic Z-burst events, although with quite
smaller conversion efficiency.
