We discuss the possibility that the extended structures, lacking young stars, routinely found in dwarf irregular galaxies (dIrr) are a consequence of a progressive shrinking of the star forming region. This would be an alternative scenario to the possible halo-disk structure of dIrr. Although the final answer must wait until kinematical data of some accuracy become available, we present two alternative approaches to the study of the extended structures in dIrrs. In the first one, the radial distribution of stellar populations together with population synthesis, based on surface brightness fluctuations (SBF), has been applied to DDO 165. This is a dIrr about 5 Mpc away from the Milky Way. Results show that the resolved, young population is more concentrated than the intermediate-old, unresolved population. The later is 7 Gyr old, in average, and has a very low metallicity (about Z = 0.0007). This indicates that, together with a truly old stellar population, an important intermediate-age population is present in the outer region of the galaxy. In our second approach, deep color-magnitude diagrams (CMDs), based on Hubble Space Telescope (HST) observations and reaching the oldest turn-offs, are used to analyze the inner and outer stellar populations of the Phoenix dwarf galaxy. Results show that, together with an old stellar population, the outer field contains also an intermediate-age population. These results are compatible with a scenario in which star forming regions are shrinking with time (the shrinking scenario). It seems more difficult to support a halo-disk scenario, which would require extended structures populated only by really old stars.