  We study the possibilities and the implications of a spontaneous breakdown of
charge in the MSSM and in the $Z_3$-symmetric NMSSM. The breakdown is triggered
by the charged states of the Higgs doublets acquiring vacuum expectation
values. In the MSSM, it is known that the presence of a charge conserving
minimum for the tree-level Higgs potential precludes a deeper (global)
charge-breaking minimum. We find that the inclusion of radiative correction to
the potential does not alter the situation while a deeper charge-conserving
minimum could arise, albeit with no major practical consequences. In the NMSSM
scenario, a charge-breaking global minimum, with or without an accompanying
charge-conserving deeper minimum, could appear even with the tree-level Higgs
potential thanks to the presence of a charge-neutral scalar state which
transforms as a singlet under the Standard Model gauge group. Use of the NMSSM
Higgs potential that includes both quantum and thermal corrections and the
requirement of a viable (stable or long-lived) vacuum that breaks the
electroweak symmetry, along with its compatibility with the latest Higgs data,
lead to nontrivial constraints on the NMSSM parameter space.
