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We reanalyse the computation of the cosmological constant $\Lambda$ at twoloops in recently proposed Superstring models without massless gravitini, bothin the theta-function based formalism and by a detailed computation in the moreexplicit hyperelliptic description of the underlying genus two Riemann surface.$\Lambda$ is expressed as the integral over the surface moduli of an amplitudewhich is zero if susy is not completely broken, but we find it to benonvanishing in the susy breaking models which can be given an explicitlyworkable fermionic formulation. Thus unfortunately the issue of gettingrealistic and perturbatively viable models from Superstring Theory remainsopen.Comment: 30 pages, Late

Evidence for nonvanishing cosmological constant in nonSUSY superstring models