  We study the general NMSSM with an emphasis on the parameter regions with a
very strong first-order electroweak phase transition (EWPT). In the presence of
heavy fields coupled to the Higgs sector, the analysis can be problematic due
to the existence of sizable radiative corrections. In this paper we propose a
subtraction scheme that helps to circumvent this problem. For simplicity we
focus on a parameter region that is by construction hidden from the current
collider searches. The analysis proves that (at least) in the identified
parameter region the EWPT can be very strong and striking gravitational wave
signals can be produced. The corresponding gravitational stochastic background
can potentially be detected at the planned space-based gravitational wave
observatory eLISA, depending on the specific experiment design that will be
approved.
