  A remarkable achievement of the realistic superstring standard--like models
is the successful prediction of the top quark mass, assuming the Minimal
Supersymmetric Standard Model spectrum below the string scale. Recently it was
shown that string scale unification requires the existence of additional
matter, in vector--like representations, at intermediate energy scales and that
certain string models contain the needed representations in their massless
spectrum. I obtain the top, bottom and tau lepton Yukawa couplings in these
models, by calculating tree level string amplitudes, in terms of the unified
gauge coupling and certain vacuum expectation values that are required for the
consistency of the string models. Using two--loop renormalization group
equations for the gauge and Yukawa couplings, I study the effect of the
intermediate matter thresholds on the top quark mass prediction. Agreement with
the experimental values of $\alpha_{\rm strong}(M_Z)$, $\sin^2\theta_W(M_Z)$
and $\alpha^{-1}_{\rm em}(M_Z)$ is imposed. It is found that the physical top
quark mass prediction is increased to the range $192-200$ GeV and that the
ratio $\lambda_b(M_Z)/\lambda_\tau(M_Z)$ is in agreement with experiment.
