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