  We study the quantum stability of Type IIB orbifold and orientifold string
models in various dimensions, including Melvin backgrounds, where supersymmetry
(SUSY) is broken {\it \`a la} Scherk-Schwarz (SS) by twisting periodicity
conditions along a circle of radius R. In particular, we compute the
R-dependence of the one-loop induced vacuum energy density $\rho(R)$, or
cosmological constant. For SS twists different from Z2 we always find, for both
orbifolds and orientifolds, a monotonic $\rho(R)<0$, eventually driving the
system to a tachyonic instability. For Z2 twists, orientifold models can have a
different behavior, leading either to a runaway decompactification limit or to
a negative minimum at a finite value R_0. The last possibility is obtained for
a 4D chiral orientifold model where a more accurate but yet preliminary
analysis seems to indicate that $R_0\to \infty$ or towards the tachyonic
instability, as the dependence on the other geometric moduli is included.
