The electric dipole moment of the muon ($d_��$) is evaluated in a two Higgs doublet model with a softly broken discrete symmetry. For $\tan��\equiv |v_2|/|v_1| \sim 1$, contributions from two loop diagrams involving the $t$ quark and the $W$ boson dominate; while for $\tan��\gsim 10$, contributions from two loop diagrams involving the $b$ quark and the $��$ lepton are dominant. For $8 \gsim \tan��\gsim 4$, significant cancellation occurs among the contributions from two loop diagrams and the one loop contribution dominates for $\tan��\sim 7$. For $\tan��\gsim 15$, the calculated $d_��$ can be close to the reach of a recently proposed experiment at the Brookhaven National Laboratory.

LaTeX, 6 pages, 1 eps figure and 2 ps figures, sprocl.sty and psfig.sty included. Talk presented by C. Kao at the 2nd International Conference on B Physics and CP Violation, Honolulu, Hawaii, USA, March 1997