  The relic abundance of stable neutralinos is investigated in $E_8 \times
E_8'$ heterotic string theory when supersymmetry is spontaneously broken by
hidden-sector gaugino condensates. In the weak coupling regime, very large
scalar masses (compared to gaugino masses) are shown to lead to a too large
relic abundance of the neutralinos, incompatible with cosmological observations
in most of parameter space. The problem does not arise in the strong coupling
regime (heterotic M-theory) because there scalar and gaugino masses are
generically of the same order of magnitude.
