X-ray flashes (XRFs) are a class of gamma-ray bursts (GRBs) with the peak energy of the time-integrated spectrum, Ep, below 30 keV, whereas classical GRBs have Ep of a few hundreds keV. Apart from Ep and the lower luminosity, the properties of XRFs are typical of the classical GRBs. Yet, the nature of XRFs and the differences from that of 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. We examine in detail the case of XRF 080330 discovered by Swift at the redshift of 1.51. This burst is representative of the XRF class and exhibits an X-ray shallow decay. The rich and broadband (from NIR to UV) photometric data set we collected across this phase makes it an ideal candidate to test the off-axis jet interpretation proposed to explain both the softness of XRFs and the shallow decay phase. We present prompt gamma-ray, early and late IR/visible/UV and X-ray observations of the XRF 080330. We derive a SED from NIR to X-ray bands across the plateau phase with a power-law index of 0.79 +- 0.01 and negligible rest-frame dust extinction. The multi-wavelength evolution of the afterglow is achromatic from ~10^2 s out to ~8x10^4 s. We describe the temporal evolution of the multi-wavelength afterglow within the context of the standard afterglow model and show that a single-component jet viewed off-axis explains the observations (abriged).
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