Various observations of dwarf starburst galaxies have revealed homogeneous abundance within the ionized region suggesting that the measured metallicities do not result from the metals ejected during the current burst (because they should not have time to mix homogeneously at such large scale) but from previous star formation episodes. It then appears that these dwarf starburst galaxies are not truly young. We propose that the metallicity observed in these objects can result only from a low but continuous star formation rate during the lifetime of galaxies. Recent observations of IZw 18 (Ostlin, 2000) seem in agreement with this scenario. We emphasize the importance of searching for a faint old underlying population in the isolated HI cloud recently detected by Kilborn et al. (2000).