  We discuss the effects of convective overshooting in the PMS evolution of
intermediate mass stars, by analysing in detail the early evolution towards the
main sequence of a 2 M_sun stellar model. These effects can be extremely
important in the end of the PMS, when the abundances in CNO elements approach
the equilibrium in the centre. We provide a possible physical explanation on
why a moderate amount of overshooting produces, as the star approaches the
ZAMS, an extra loop in the evolutionary tracks on the HR diagram.
  An interesting feature is that there is a very well defined amount of
overshooting (for a given stellar mass and chemical composition) beyond which a
loop is produced. For smaller amounts of overshooting such a loop does not take
place and the evolutionary tracks are similar to the ones obtained by Iben
(1965). The amount of overshooting needed to produce the loop decreases with
stellar mass.
  We discuss the underlining physical reasons for the behaviour predicted by
the evolution models and argue that it provides a crucial observational test
for convective overshooting in the core of intermediate mass stars.
