  The phenomenology of the explicit CP violation in the Higgs sector of the
next-to-minimal supersymmetric standard model (NMSSM) is investigated, with
emphasis on the charged Higgs boson. The radiative corrections due to both
quarks and scalar-quarks of the third generation are taken into account, and
the negative result of the search for the Higgs bosons at CERN LEP2, with the
discovery limit of 0.1 pb, is imposed as a constraint. It is found that there
are parameter regions of the NMSSM where the lightest neutral Higgs boson may
even be massless, without being detected at LEP2. This implies that the LEP2
data do not contradict the existence of a massless neutral Higgs boson in the
NMSSM. For the charged Higgs boson, the radiative corrections to its mass may
be negative in some parameter regions of the NMSSM. The phenomenological lower
bound on the radiatively corrected mass of the charged Higgs boson is increased
as the CP violation becomes maximal, i.e., as the CP violating phase becomes
$\pi/2$. At the maximal CP violation, its lower bound is about 110 GeV for 5
$\leqslant \tan \beta \leqslant$ 40. The vacuum expectation value (VEV) of the
neutral Higgs singlet is shown to be no smaller than 16 GeV for any parameter
values of the NMSSM with explicit CP violation. This value of the lower limit
is found to increase up to about 45 GeV as the ratio ($\tan \beta$) of the VEVs
of the two Higgs doublets decreases to smaller values ($\sim$ 2). The discovery
limit of the Higgs boson search at LEP2 is found to cover about a half of the
kinematically allowed part of the whole parameter space of the NMSSM, and the
portion is roughly stable against the CP violating phase.
