The strange quark mass is calculated from QCD sum rules for the diverg
ence of the vector as well as axial-vector current in the next-next-to
-leading logarithmic approximation. The determination for the divergen
ce of the axial-vector current is found to be unreliable due to large
uncertainties in the hadronic parametrisation of the two-point functio
n. From the sum rule for the divergence of the Vector current, we obta
in a value of m(s) = ($) over bar m(s)(1 GeV) = 189 +/- 32 MeV, where
the error is dominated by the unknown perturbative O(alpha(s)(3)) corr
ection. Assuming a continued geometric growth of the perturbation seri
es, we find m(s) = 178 +/- 18 MeV. Using both determinations of m(s),
together with quark-mass ratios from chiral perturbation theory, we al
so give estimates of the light quark masses m(u) and m(d).