  The strange quark mass is calculated from QCD sum rules for the divergence of
the vector as well as axial-vector current in the next-next-to-leading
logarithmic approximation. The determination for the divergence of the
axial-vector current is found to be unreliable due to large uncertainties in
the hadronic parametrisation of the two-point function.
  From the sum rule for the divergence of the vector current, we obtain a value
of $m_s\equiv\mb_s(1\,\gev)=189\pm32\,\mev$, where the error is dominated by
the unknown perturbative ${\cal O}(\alpha_s^3)$ correction. Assuming a
continued geometric growth of the perturbation series, we find
$m_s=178\pm18\,\mev$. Using both determinations of $m_s$, together with
quark-mass ratios from chiral perturbation theory, we also give estimates of
the light quark masses $m_u$ and $m_d$.
