We argue that the lightest supersymmetric particles (LSP) can be produ
ced with extremely high energies E greater than or similar to 10(10) G
eV in the Universe at the present epoch. Their most probable sources a
re decaying superheavy particles produced by topological defects or as
relic Big Bang particle. We discuss the mechanisms of production of L
SP at ultra-high energies (UHE) and the interaction of the UHE LSP wit
h matter. The most attention is given to the neutralino as LSP, althou
gh the gluino is also considered as a phenomenological possibility. (C
) 1998 Published by Elsevier Science B.V.