  Compact analytic expressions have been obtained for the first order
perturbative QCD corrections to the inclusive spectra of the leptons in the
semileptonic decays of polarised heavy quarks. Charmed and beautiful $\Lambda$
baryons from $Z^0$ decays can be viewed as sources of highly polarised charm
and bottom quarks. Charged leptons and neutrinos from $\Lambda_b$ and
$\Lambda_c$ decays can be used in the polarisation studies for the
corresponding heavy quarks. Thus our results are applicable for the b quark
polarisation measurements at LEP. Short lifetime enables polarisation studies
for the top quark. The angular-energy spectra of the charged leptons are
particularly useful in this respect whereas the distributions of the neutrinos
are sensitive to deviations from the V-A structure of the charged weak current
in the decay.
