We study the constraints on the parameter space of the supersymmetric stand
ard model extended by a gauge singlet, which arise from the absence of glob
al minima of the effective potential with slepton or squark vevs. Particula
r attention is paid to the so-called "UFB" directions in field space, which
are F-flat in the MSSM. Although these directions are no longer F-flat in
the (M + 1)SSM, we show that the corresponding MSSM-like constraints on m(0
)/M-1/2 apply also to the (M + I)SSM. The net effect of all constraints on
the parameter space are more dramatic than in the MSSM. We discuss the phen
omenological implications of these constraints. (C) 1999 Elsevier Science B
.V. All rights reserved.