We search for hadronic decays of a light Higgs boson (A0) produced in radiative decays of an Upsilon(2S) or Upsilon(3S) meson, Upsilon --> gamma A0. The data have been recorded by the BABAR experiment at the Upsilon(3S) and Upsilon(2S) center of mass energies, and include (121.3 pm 1.2) x 10^6 Upsilon(3S) and (98.3 pm 0.9) x 10^6 Upsilon(2S) mesons. No significant signal is observed. We set 90% confidence level upper limits on the product branching fractions B(Upsilon(nS)-->gamma A0) x B(A0-->hadrons) (n=2 or 3) that range from 1 x 10^{-6} for an A0 mass of 0.3 GeV/c^2 to 8 x 10^{-5} at 7 GeV/c^2.
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