  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 $<2.5\times10^{20}$
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.
