The recent measurement of the muon anomalous magnetic moment a(mu) shows a
2.6 sigma deviation from the standard model value. We show that it puts str
ong constraints on the parameter space of the two-Higgs-doublet model (2HDM
) II. The dominant contribution of the Higgs bosons comes at the mo-loop le
vel. and in order to explain the data it favors a pseudoscalar A with a lig
ht mass range and a large tan beta. At 95% C.L., the upper limit for m(A) i
s 29 (55) (85) GeV for tan beta = 30 (45) (60), and tan beta is bounded bel
ow at 17. This is in sharp contrast to the conclusion one draws from consid
ering one-loop Higgs contributions alone. Finally, we also discuss the role
of the Higgs contributions in the minimal supersymmetric standard model.