  We calculate ~$\sin^2\theta(M_Z)$ ~in the MSSM in terms of ~ $\alpha_{EM}$,
~$G_F$, ~$m_t$, ~$\tan\beta$ ~and SUSY mass parameters with the same accuracy
as the present calculations of ~$\sin^2\theta(M_Z)$ ~in the SM. We compare the
results with the standard leading logarithmic approximation used for SUSY
threshold corrections and find important differences in the case of light
sparticles. We give approximate formulae connecting coupling constants in the
SM and in the MSSM and comment on process dependence of such formulae. The
obtained values of the MSSM couplings ~$\alpha_i(M_Z)$ ~are used to investigate
gauge coupling unification in the minimal SUSY ~SU(5) ~model. Our
non-logarithmic corrections lower the predicted value of the Higgs triplet
mass. The interplay between the supersymmetric and GUT thresholds in achieving
unification for the coupling constants in the range of the experimentally
acceptable values is quantified.
