  We reanalyse the computation of the cosmological constant $\Lambda$ at two
loops in recently proposed Superstring models without massless gravitini, both
in the theta-function based formalism and by a detailed computation in the more
explicit hyperelliptic description of the underlying genus two Riemann surface.
$\Lambda$ is expressed as the integral over the surface moduli of an amplitude
which is zero if susy is not completely broken, but we find it to be
nonvanishing in the susy breaking models which can be given an explicitly
workable fermionic formulation. Thus unfortunately the issue of getting
realistic and perturbatively viable models from Superstring Theory remains
open.
