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 \times 10 ^ { -14 } erg cm ^ { -2 } s ^ { -1 } ( 0.2-10 keV ) . The spectrum is a power law with photon index \Gamma =1.9 and absorption < 2.5 \times 10 ^ { 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 \sim 10 below simultaneous measurements . This is likely due to the presence of SN2003dh .