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We have generated x-ray radiation from the nonlinear Thomson scattering of a 30 fs/1.5 J laser beam on plasma electrons. A collimated x-ray radiation with a broad continuous spectrum peaked at 0.15 keV with a significant tail up to 2 keV has been observed. These characteristics are found to depend strongly on the laser strength parameter a0. This radiative process is dominant for a0 greater than unity at which point the relativistic scattering of the laser light originates from MeV energy electrons inside the plasma.