In supersymmetric models the presence of Higgs triplets introduce new quart
ic interactions for the doublets that may raise the mass of the lightest CP
-even field up to 205 GeV. We show that the complete effect of the triplets
can be understood by decoupling them from the minimal sector and then anal
yzing the vacuum and the spectrum of the effective two-Higgs doubler model
that results. We find that the maximum value of m(h) is only achieved in a
very definite region of the parameter space. In this region, however, radia
tive corrections decrease the bound to approximate to 190 GeV. (C) 1998 Els
evier Science B.V. All rights reserved.