  We present the up to now most precise evaluation of electroweak and
supersymmetric contributions to the anomalous magnetic moment of the muon \amu,
describing in detail also the calculational techniques. We calculate the
bosonic two-loop contributions in the Standard Model without the approximation
of a heavy Higgs-boson mass, finding corrections up to 0.2*10^{-10} for a light
Higgs boson. In the Minimal Supersymmetric Standard Model the corresponding
two-loop contributions from the two-Higgs-doublet model part differ from the
Standard Model result by up to 0.3*10^{-10}. Finally, we evaluate the diagrams
where a loop of charginos or neutralinos, the superpartners of gauge and Higgs
bosons, is inserted into a two-Higgs-doublet one-loop diagram. These
corrections can amount up to 10*10^{-10}, which is almost 2\sigma of the
current experimental uncertainty.
