Recently, huge photometric databases are being obtained for the Magellanic Clouds and other Local Group galaxies. These data allow, not only to study in great detail the star formation history of these systems, but also provide important information on details of stellar evolution theory. In the case of the LMC, two structures not previously noticed in color magnitude diagrams have been interpreted by Zaritszky & Lin (1997) and Alcock et al (1997) as the possible signature of an intervening population towards the LMC. Beaulieu & Sackett (1997) have shown that one of them corresponds to the location of the blue loops of few Myr old stars. In this paper we show that the other one, associated till now with the RGB-bump predicted by theory and observed in globular clusters, is actually produced during the AGB evolution. We will call this newly observed structure AGB-bump. In addition to the LMC, the AGB-bump has been observed in some M 31 halo fields and in some well populated color-magnitude diagrams of dSph galaxies and globular clusters. The AGB-bump is produced when low and intermediate-mass stars approach the Hayashi Line at the beginning of the AGB phase. The penetration and posterior recession of the convective envelope slows down the evolution of the star momentarily, producing changes in the luminosity function of the stars. These changes are very small, and have been detected only when the stellar samples are large enough. We will compare the stellar evolution predictions of the position and strength of the AGB-bump with the observed structures in the LMC, in M 31 and in globular clusters.