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We consider a class of heterotic N=2 -> 0 super no-scale Z_2-orbifold models.An appropriate stringy Scherk-Schwarz supersymmetry breaking induces tree levelmasses to all massless bosons of the twisted hypermultiplets and thereforestabilizes all twisted moduli. At high supersymmetry breaking scale, thetachyons that occur in the N=4 -> 0 parent theories are projected out, and noHagedorn-like instability takes place in the N=2 -> 0 models (for small enoughmarginal deformations). At low supersymmetry breaking scale, the stability ofthe untwisted moduli is studied at the quantum level by taking into accountboth untwisted and twisted contributions to the 1-loop effective potential. Thelatter depends on the specific branch of the gauge theory along which thebackground can be deformed. We derive its expression in terms of all classicalmarginal deformations in the pure Coulomb phase, and in some mixedCoulomb/Higgs phases. In this class of models, the super no-scale conditionrequires having at the massless level equal numbers of untwisted bosonic andtwisted fermionic degrees of freedom. Finally, we show that N=1 -> 0 superno-scale models are obtained by implementing a second Z_2 orbifold twist on N=2-> 0 super no-scale Z_2-orbifold models.

N=2 -> 0 super no-scale models and moduli quantum stability