  Each time diffusion of elements is invoked in explaining abundance anomalies
in a star, this supposes implicitly that a stratification process is in
progress somewhere in that star. This means also, that the element abundances
can still be evolving according to the star's age and fundamental parameters.
Moreover, it has been shown that the superficial abundances may have complex
temporal behavior. This should be detectable through new observations. In some
cases, it may be already apparent in available data.
  The building up of the elements' stratification is a very difficult process
to study. This is due to the existence of strong non-linearities in the
time-dependent equations, which must be solved numerically. We will discuss
some works that tackle this problem for Ap and Am stars, and we will present
some results concerning mostly Am stars. Future desirable improvements in these
studies will be considered.
