Bhabha scattering with higher order weak loop corrections

We present a compact incorporation of the weak loop effects in the Bhabha cross section with the accuracy required by the present precision experiments. Special care is taken of the leading 2-loop effects from a heavy top quark which are of the type α2(mt/MZ)4. We find very satisfactory agreement between two independent calculations which are based on different gauges and different renormalizations. The compact formulation in terms of form factors allows a straight-forward implementation into analytic or Monte Carlo QED calculations. (orig.)