We report on XMM-Newton and Rossi-XTE observations of the bright (fluence $sim$ 10$^{-4}$ erg cm$^{-2}$) and nearby (z=0.1685) Gamma-Ray Burst GRB030329 associated to SN2003dh. The first Rossi-XTE observation, 5 hours after the burst, shows a flux decreasing with time as a power law with index 0.9$pm$0.3. Such a decay law is only marginally consistent with a further Rossi-XTE measurement (at t-t$_{GRB}sim$30 hr). Late time observations of this bright afterglow at X-ray wavelengths have the advantage, compared to optical observations, of not being affected by contributions from the supernova and host galaxy. A first XMM-Newton observation, at t-t$_{GRB}sim$37 days, shows a flux of 4$times10^{-14}$ erg cm$^{-2}$ s$^{-1}$ (0.2-10 keV). The spectrum is a power law with photon index $Gamma$=1.9 and absorption $<2.5times10^{20}$ cm$^{-2}$, consistent with the Galactic value. A further XMM-Newton pointing at t-t$_{GRB}sim$61 days shows a flux fainter by a factor $sim$2. The combined Rossi-XTE and XMM-Newton measurements require a break at t$sim$0.5 days in the afterglow decay, with a power law index increasing from 0.9 to 1.9, similar to what is observed in the early part of the optical afterglow. The extrapolation of the XMM-Newton spectra to optical frequencies lies a factor of $sim10$ below simultaneous measurements. This is likely due to the presence of SN2003dh.
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