  When supersymmetry is spontaneously broken at tree level, the spectrum of the
heterotic string compactified on orbifolds of tori contains an infinite number
of potentially tachyonic modes. We show that this implies instabilities of
Minkowski spacetime, when the scale of supersymmetry breaking is of the order
of the string scale. We derive the phase space structure of vacua in the case
where the tachyonic spectrum contains a mode with trivial momenta and winding
numbers along the internal directions not involved in the supersymmetry
breaking.
