  We present deep J,H,Ks photometry and accurate Color Magnitude Diagrams down
to K ~18.5, for a sample of 13 globular clusters in the Large Magellanic Cloud.
This data set combined with the previous sample of 6 clusters published by our
group gives the opportunity to study the properties of giant stars in clusters
with different ages (ranging from ~80 Myr up to ~3.5 Gyr). Quantitative
estimates of star population ratios (by number and luminosity) in the
Asymptotic Giant Branch, the Red Giant Branch and the He-clump, have been
obtained and compared with theoretical models in the framework of probing the
so-called phase transitions. The AGB contribution to the total luminosity
starts to be significant at ~200 Myr and reaches its maximum at ~5-600 Myr,
when the RGB Phase Transition is starting. At ~900 Myr the full developing of
an extended and well populated RGB has been completed. Both the occurrence of
the AGB and RGB Phase Transitions are sharp events, lasting a few hundreds Myr
only. These empirical results agree very well with the theoretical predictions
of simple stellar population models based on canonical tracks and the
fuel-consumption approach.
