Context. X-ray flashes (XRFs) are a class of gamma-ray bursts (GRBs) with a peak energy of the time-integrated spectrum, E_{p_{, typically below 30 keV, whereas classical GRBs have E_{p_{of a few hundreds of keV. Apart from E_{p_{and the systematically lower luminosity, the properties of XRFs, such as their duration or spectral indices, are typical of the classical GRBs. Yet, the nature of XRFs and their differences from GRBs are not understood. In addition, there is no consensus on the interpretation of the shallow decay phase observed in most X-ray afterglows of both XRFs and GRBs.Aims. We examine in detail the case of XRF 080330 discovered by Swift at redshift 1.51. This burst is representative of the XRF class and exhibits an X-ray shallow decay. The rich broadband (from NIR to UV) photometric data set we collected during this phase makes it an ideal candidate for testing the off-axis jet interpretation proposed to explain both the softness of XRFs and the shallow decay phase.Methods. We present prompt γ-ray, early and late NIR/visible/UV and X-ray observations of the XRF 080330. We derive a spectral energy distribution from NIR to X-ray bands across the shallow/plateau phase and describe the temporal evolution of the multi-wavelength afterglow within the context of the standard afterglow model.Results. The multiwavelength evolution of the afterglow is achromatic from ~10^{2^{s to ~810^{4^{s. The energy spectrum from NIR to X-ray is reproduced well by a simple power-law, , with = 0.79±0.01 and negligible rest-frame dust extinction. The light curve can be modelled by either a piecewise power-law or the combination of a smoothly broken power law with an initial rise up to ~600 s, a plateau lasting up to ~2 ks, followed by a gradual steepening to a power-law decay index of ~2 until 82 ks. At this point, a bump appears to be modelled well with a second component, while the corresponding optical energy spectrum, , reddens by = 0.26±0.06.Conclusions. A single-component jet viewed off-axis can explain the light curve of XRF 080330, the late-time reddening being due to the reverse shock of an energy injection episode and its being an XRF. Other possibilities, such as the optical rise marking the pre-deceleration of the fireball within a wind environment, cannot be excluded definitely, but appear to be contrived. We exclude the possibility of a dust decreasing column density being swept up by the fireball as explaining the rise of the afterglow.}}}}}}}}}}

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