  There are nowadays strong experimental constraints on supersymmetric theories
from the Higgs measurements as well as from the null results in Sparticle
searches. However, even the parameter spaces which are in agreement with
experimental data can be further constrained by using theoretical
considerations. Here, we discuss for the MSSM and NMSSM the impact of
perturbative unitarity as well as of the stability of the one-loop effective
potential. We find in the case of the MSSM, that vacuum stability is always the
stronger constraint. On the other side, the situation is more diverse in the
NMSSM and one should always check both kind of constraints.
