  We predict the behaviour of the abundances of $\alpha$-elements and iron in
the intracluster medium as a function of redshift in poor and rich clusters. In
order to do that we calculate the detailed chemical evolution of elliptical
galaxies by means of one-zone and multi-zone models and then we integrate the
contributions to the total gas and single elements by ellipticals over the
cluster mass function at any given cosmic time which is then transformed into
redshift according to the considered cosmological model. We refer to the
one-zone model for ellipticals as to burst model and to the multi-zone model as
to continuous model. We find that in the case of the burst model the ICM
abundances should be quite constant starting from high redshifts ($z > 2$) up
to now, whereas in the continuous model the ICM abundances should increase up
to $z \sim 1$ and are almost constant from $z \sim 1$ up to $z=0$. Particular
attention is devoted to the predictions of the $[\alpha/Fe]_{ICM}$ ratio in the
ICM: for the burst model we predict $[\alpha/Fe]_{ICM}>0$ over the whole range
of redshifts and in particular at $z =0$, whereas in the case of the continuous
model we predict a decreasing $[\alpha/Fe]_{ICM}$ ratio with decreasing $z$ and
$[\alpha/Fe]_{ICM} \le 0$ at $z= 0$. In particular, we predict
$[O/Fe]_{ICM}(z=0) \le +0.35$ dex and $[Si/Fe]_{ICM}(z=0) \le +0.15$ dex for
the bursts models and $[O/Fe]_{ICM}(z=0) \le -0.05$ dex and $[Si/Fe]_{ICM}(z=0)
\le +0.13$ dex for the continuous models, the precise values depending on the
assumed cosmology. Finally, we discuss the influence of different cosmologies
on the results.
