  We investigate the existence of string vacua with Massive Spectrum Degeneracy
Symmetry (MSDS) in Heterotic and Type II orbifold constructions. We present a
classification of all possible Z_2^N-orbifolds with MSDS symmetry that can be
constructed in the formalism of the 2d free fermionic construction. We
explicitly construct several two-dimensional models whose Reduced Massive
Spectrum Degeneracy Symmetry (RMSDS) is due to a set of Z_2-orbifold
projections induced naturally in the framework of the free fermionic
construction. In all proposed models the massive boson and fermion degrees of
freedom exhibit Massive Spectrum Degeneracy Symmetry while the number of
massless bosons n(b) and massless fermions n(f) are different; n(b) neq n(f).
This property distinguishes the MSDS Z_2-twisted theories from ordinary
supersymmetric ones. Some comments are stated concerning the large marginal (J
x barJ)-deformations of the proposed models connecting them to
higher-dimensional gauged-supergravity theories with non-trivial geometrical
fluxes.
