  We present the full O(alpha_s) longitudinal spin-spin correlations for
heavy-quark pair production at e+ e- high-energy colliders in closed analytical
form. In such reactions, quark and antiquark have strongly correlated spins,
and the longitudinal components are dominant. For the explicit computation of
the QCD bremsstrahlung contributions, new phase-space integrals are derived.
Explicit numerical estimates are given for t t_bar and b b_bar production.
Around the Z-peak, QCD one-loop corrections depolarize the spin-spin asymmetry
for bottom quark pairs by approximately -4%. For top pair production, we find
at 350GeV a 0.6% increased polarization over a value of 0.4 in the longitudinal
correlation. For more than 1 TeV the O(alpha_s) corrections enhance
depolarization to -2% in the top-pair case.
