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<jats:title>ABSTRACT</jats:title> <jats:p>We present an <jats:italic>INTEGRAL</jats:italic> spectral analysis in the orbital/superorbital phase space of LS I +61°303. A hard X-ray spectrum with no cutoff is observed at all orbital/superorbital phases. The hard X-ray index is found to be uncorrelated with the radio index (non-simultaneously) measured at the same orbital and superorbital phases. In particular, the absence of an X-ray spectrum softening during periods of negative radio index does not favor a simple interpretation of the radio index variations in terms of a microquasar's changes of state. We uncover hints of superorbital variability in the hard X-ray flux, in phase with the superorbital modulation in soft X-rays. An orbital phase drift of the radio peak flux and index along the superorbital period is observed in the radio data. We explore its influence on a previously reported double-peak structure of a radio orbital light curve, and present it as a plausible explanation.</jats:p>