Development of the advanced compositions and technologies for the production of alloys based on aluminium with rare-earth metals (REM) creates competition for materials based on heavier and more refractory (iron) as well as expensive metals (copper, titanium). When alloy melting under conditions of ordinary overheating up to 100 K and its cooling at low rates $v$ $\cong$ 1-10 K/s, the formation of fine grain ($\cong$ 10 µm) is complicated. Use of induction melting in the magnetodynamic aggregate of the Al-Cu-alloy base, followed by remelting in an electric-resistance furnace with the addition of rare-earth metals, made it possible to use low overheating. At $v$ = 4, 10, and 30 K/s, grains with a size of 36.0, 17.1 and 11.6 µm, respectively, were formed in the alloy. The imposition of a constant magnetic field on the melt during its cooling and solidification made it possible to obtain a grain with a size of 11.0 µm at $v$ = 10 K/s. These are investigated: the effect of the field on the concentration of components in the grains, the range of the content of elements in the microvolumes of the grain, the difference in concentration between the centre and the periphery of the grain. As found, the effect of the field on the redistribution in the paramagnetic base (Al) of diamagnetic Cu, Zn, Pb, paramagnetic Sn, Mn, Zr, Ce, La, Nd, Pr and ferromagnetic Fe is associated with their content in the alloy, magnetic susceptibility, atom radius and mass. Under the influence of the field in the volume of grains, there are both the decrease in the content of Pb, which has the lowest magnetic susceptibility among the alloy components, and the increase in the content of Fe, which is a component with the highest magnetic susceptibility. The effect of the field on the rest of the alloy components is complex. Because of the action of the field, the content of Cu and Fe in the grains is increased, and the amount of Ce, La and Nd in their microvolumes is increased. The segregation of Sn and Pb at the grain periphery is eliminated.