  We study the properties of the Higgs and supersymmetric particle spectrum
associated with the infrared fixed point solution of the top quark mass in the
MSSM. We concentrate on the possible detection of these particles, analysing
the deviations from the Standard Model predictions for the leptonic and
hadronic variables measured at LEP and for the decay rate $b\rightarrow
s\gamma$. We consider the low and moderate $\tan \beta$ regime, and we study
both, the cases of universal and non--universal soft supersymmetry breaking
parameters at high energies. In the first case, for any given value of the top
quark mass, the Higgs and sparticle spectra are completely determined as a
function of two soft supersymmetry breaking parameters. In the case of
non--universality, instead, the strong correlations between the sparticle
masses are relaxed, allowing a richer structure for the precision data
variables. We show, however, that the requirement that the low energy theory
proceeds from a grand unified theory with a local symmetry group including
$SU(5)$, strongly constrains the set of possible indirect experimental
signatures. As a general feature, whenever a significant deviation from the
Standard Model value of the precision data variables is predicted, a light
sparticle, visible at LEP2, appears in the spectrum.
