We present a detailed study of the stellar and HI structure of the dwarf irregular galaxies SextansA and SextansB, members of the NGC3109 association. We use newly obtained deep (r~26.5) and wide field g,r photometry to extend the Surface Brightness (SB) profiles of the two galaxies down to mu_V~ 31.0 mag/arcsec^2. We find that both galaxies are significantly more extended than what previously traced with surface photometry, out to ~4 kpc from their centers along their major axis. Older stars are found to have more extended distribution with respect to younger populations. We obtain the first estimate of the mean metallicity for the old stars in SexB, from the color distribution of the Red Giant Branch, <[Fe/H]>=-1.6. The SB profiles show significant changes of slope and cannot be fitted with a single Sersic model. Both galaxies have HI discs as massive as their respective stellar components. In both cases the HI discs display solid-body rotation with maximum amplitude of ~50 km/s (albeit with significant uncertainty due to the poorly constrained inclination), implying a dynamical mass ~10^{9}~M_sun, a mass-to-light ratio M/L_V~25 and a dark-to-barionic mass ratio of ~10. The distribution of the stellar components is more extended than the gaseous disc in both galaxies. We find that the main, approximately round-shaped, stellar body of Sex~A is surrounded by an elongated low-SB stellar halo that can be interpreted as a tidal tail, similar to that found in another member of the same association (Antlia). We discuss these, as well as other evidences of tidal disturbance, in the framework of a past passage of the NGC3109 association close to the Milky Way, that has been hypothesized by several authors and is also supported by the recently discovered filamentary configuration of the association itself.
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