Upward-going muon events collected with the lower half of the MACRO de
tector have been analyzed in order to search for Weakly Interacting Ma
ssive Particles possibly trapped in the core of the Sun and of the Ear
th. No statistically significant signal could be discriminated over th
e possible fluctuations of the atmospheric neutrino background. Assumi
ng a particular neutralino model, the explorable neutralino mass regio
n has been considered.