  We calculate the dominant contributions to the muon $g-2$ at the two-loop
level due to a generic pseudoscalar boson that may exist in any exotic Higgs
sector in most extensions of the standard model. The leading effect comes from
diagrams of the Barr-Zee type. A sufficiently light pseudoscalar Higgs boson
can give rise to contribution as large as the electroweak contribution which is
measurable in the next round of $g-2$ experiment. Through the contribution we
calculated here, the anticipated improved data in the recent future on the muon
$g-2$ can put the best limit on the possible existence of a light pseudoscalar
boson in physics beyond the standard model.
