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We report the results of XMM-Newton and BeppoSAX observations of the radioand X-ray emitting star LS I +61 303, likely associated with the gamma-raysource 2CG 135+01 and recently detected also at TeV energies. The data includea long XMM-Newton pointing carried out in January 2005, which provides thedeepest look ever obtained for this object in the 0.3-12 keV range. During thisobservation the source flux decreased from a high level of 13E12 erg/cm2/s to4E12 erg/cm2/s within 2-3 hours.This flux range is the same seen in shorter andless sensitive observations carried out in the past, but the new data show forthe first time that transitions between the two levels can occur on short timescales. The flux decrease was accompanied by a significant softening of thespectrum, which is well described by a power law with photon index changingfrom 1.62+/-0.1 to 1.83+/-0.1. A correlation between hardness and intensity isalso found when comparing different short observations spanning almost 10 yearsand covering various orbital phases.LS I +61 303 was detected in the 15-70 keVrange with the PDS instrument in one of the BeppoSAX observations, providingevidence for variability also in the hard X-ray range. The X-ray spectra,discussed in the context of multiwavelength observations, place someinteresting constraints on the properties and location of the high-energyemitting region.Comment: Revised version, accepted for publication in A&A. Updated references,  few typos corrected, minor changes following referee's suggestion

XMM-Newton observation of a spectral state transition in the peculiar radio/X-ray/γ-ray source LS I +61 303