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We have observed the X-ray radiation produced by the nonlinear Thomson scattering of an intense femtosecond laser on relativistic electrons. The 1 J 30 fs laser beam is focussed on a helium gas jet and the X-ray radiation is detected using a grazing incidence X-ray spectrometer. The analysis of the data shows that the effect of the plasma as well as the additional acceleration of the electrons inside the plasma waves should be taken into account to fit the experimental results.