  In the electroweak phase transition there arises the problem of baryon number
washout by sphaleron transitions, which can be avoided if the phase transition
is strongly enough first order. The phase transition in the Standard Model or
in the Minimal Supersymmetric Standard Model seems to be too weak to suppress
the sphaleron transitions sufficiently. We report here on an investigation of
the Next to Minimal Supersymmetric Standard Model, NMSSM, which contains a
Higgs singlet N in addition to the two Higgs doublets of the minimal SUSY
model. This next to minimal model has the helpful new feature that the Higgs
potential contains a tree level trilinear field term. We consider the most
general form of the Higgs potential without imposing a discrete symmetry; in
particular we allow the presence of a mu-term in the superpotential. We find
that electroweak baryon preservation is compatible with the NMSSM.
