We calculate the dominant contributions to the muon g-2 at the two-loop lev
el due to a generic pseudoscalar boson that may exist in any exotic Higgs s
ector in most extensions of the standard model. The leading effect comes fr
om diagrams of the Barr-Zee type. A sufficiently light pseudoscalar Higgs b
oson can give rise to contributions as large as the electroweak contributio
n which is measurable in the next round of g-2 experiments. Through the con
tribution we calculate here, the anticipated improved data in the recent fu
ture 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.