  We provide analytical results for the $O(\alpha_s)$ corrections to the polar
angle dependence of the longitudinal spin-spin correlation asymmetry in
$e^+e^-\to q\bar q$. For top quark pair production the $O(\alpha_s)$
corrections to the longitudinal spin-spin asymmetry are strongly polar angle
dependent and can amount up to $4\%$ in the $q^2$-range from above $t\bar t$
threshold up to $\sqrt{q^2}=1000$ GeV. The $O(\alpha_s)$ radiative corrections
to the correlation asymmetry are below $1\%$ in the forward direction where the
cross section is largest. In the $e^+e^-\to b\bar b$ case the $O(\alpha_s)$
corrections reduce the asymmetry value from its $m_b=0$ value of $-100\%$ to
approximately $-96\%$ for $q^2$-values around the $Z$ peak and are practically
independent of the value of the polar angle theta. This reduction can be traced
to finite anomalous contributions from residual mass effects which survive the
$m_b\to 0$ limit. We discuss the role of the anomalous contributions and the
pattern of how they contribute to spin-flip and non-flip terms.
