We report the results of XMM-Newton and BeppoSAX observations of the radio and X–ray emitting star LS I +61 303 , likely associated with the gamma-ray source 2CG 135+01 and recently detected also at TeV energies . The data include a long XMM-Newton pointing carried out in January 2005 , which provides the deepest look ever obtained for this object in the 0.3–12 keV range . During this observation the source flux decreased from a high level of \sim 13 \times 10 ^ { -12 } erg cm ^ { -2 } s ^ { -1 } to 4 \times 10 ^ { -12 } erg cm ^ { -2 } s ^ { -1 } within 2-3 hours . This flux range is the same seen in shorter and less sensitive observations carried out in the past , but the new data show for the first time that transitions between the two levels can occur on short time scales . The flux decrease was accompanied by a significant softening of the spectrum , which is well described by a power law with photon index changing from 1.62 \pm { 0.01 } to 1.83 \pm { 0.01 } . A correlation between hardness and intensity is also found when comparing different short observations spanning almost 10 years and covering various orbital phases . LS I +61 303 was detected in the 15–70 keV range with the PDS instrument in one of the BeppoSAX observations , providing evidence for variability also in the hard X–ray range . The X–ray spectra , discussed in the context of multiwavelength observations , place some interesting constraints on the properties and location of the high-energy emitting region .