We describe some specific but reasonable conditions for the formation of superdense clumps (or minihalos) of dark matter. Such clumps can be produced by several mechanisms, most notably by spiky features in the spectrum of density perturbations. Being produced very early during the radiation-dominated epoch, these clumps evolve as isolated objects. They do not belong to hierarchical structures for a long time after production and are therefore not destroyed by tidal interactions during the formation of larger structures. If the clumps are constituted of superheavy dark matter particles, then the evolution of their central part can lead to a "gravithermal catastrophe," increasing the central density and thus the annihilation signal. As a result, annihilations of superheavy neutralinos in dense clumps may lead to observable fluxes of annihilation products in the form of ultrahigh-energy particles.
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