  We have analyzed a sample of LBGs from z =3.5 to z=6 selected from the
GOODS-S field as B,V and i-dropouts, and with spectroscopic observations
showing that they have the Lyalpha line in emission. Our main aim is to
investigate their physical properties and their dependence on the emission line
characteristics, to shed light on the relation between galaxies with Lyalpha
emission and the general LBG population.The objects were selected from their
continuum colors and then spectroscopically confirmed by the GOODS
collaboration and other campaigns. From the spectra we derived the line flux
and EW. We then used U-band to mid-IR photometry from GOODS-MUSIC to derive the
physical properties of the galaxies, such as total stellar mass, age and so on,
through standard SED fitting techniques.Although most galaxies are fit by young
stellar populations, a small but non negligible fraction has SEDs that require
considerably older stellar component, up to 1 Gyr. There is no apparent
relation between age and EW: some of the oldest galaxies have large EW, and
should be also selected in narrow band surveys. Therefore not all Lyalpha
emitters are primeval galaxies in the very early stages of formation,as is
commonly assumed. We also find a large range of stellar populations, with
masses from 5x10^8 Msol to 5x10^10 Msol and SFR from few to 60 Msol/yr.
Although there is no correlation between mass and EW, we find a significant
lack of massive galaxies with high EW, which could be explained if the most
massive galaxies were more dusty and/or contained more neutral gas than less
massive objects. Finally we find that more than half of the galaxies contain
small but non negligible amounts of dust: the mean E(B-V) and the EW are well
correlated, although with a large scatter, as already found at lower redshift
