  The vacuum polarization functions $\Pi(q^2)$ of charged and neutral gauge
bosons which arise from top and bottom quark loops lead to important shifts in
relations between electroweak parameters which can be measured with
ever-increasing precision. The large mass of the top quark allows approximation
of these functions through the first two terms of an expansion in
$M_Z^2/M_t^2$. The first three terms of the Taylor series of $\Pi(q^2)$ are
evaluated analytically up to order $\as^2$. The first two are required to
derive the approximation, the third can be used to demonstrate the smallness of
the neglected terms. The paper improves earlier results based on the leading
term $\propto G_F M_t^2 \as^2$. Results for the subleading contributions to
$\dr$ and the effective mixing angle $\sineff$ are presented.
