We predict the behaviour of the abundances of ff- elements and iron in the intracluster medium (ICM) 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. In the case of the multi-zone model for ellipticals the more external regions evolve much faster than the internal ones which maintain a very low level of star formation almost until the present time. In other words, the outermost regions develop a galactic wind, after which the region evolves passively, at much earlier times than the innermost regions as opposed to the classic one-zone model where the galactic wind develops at early times over the whole galaxy.We refer to the one-zone model 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 ~ 1 and are almost constant from z ~ 1 up to z = 0. Particular attention is devoted to the predictions of the [ff=Fe]ICM ratio in the ICM: for the burst model we predict [ff=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 [ff=Fe]ICM ratio with decreasing z and [ff=Fe]ICM < 0 at z = 0. In particular, we predict [O=Fe]ICM(z = 0) < +0:35 dex and [Si=F e]ICM(z = 0) < +0:15 dex for the burst models and [O=Fe]ICM(z = 0) <−0:05 dex and [Si=F e]ICM(z = 0) < +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.