The addition of REM (rare earth metals) to Al alloys increases their operational and technological properties. The alloys strength increases with increasing in the additive amount, while their density remains relatively low. Such alloys held promise for use as structural and electrical materials. The problem of obtaining cast aluminium alloys of hypereutectic composition at low cooling rates ($v$) of conventional casting methods ($v \leq$ 100°C/s) is the formation of intermetallic compounds with sizes of more than 100 $\mu$m with faceting of extended surfaces. The effect of a constant magnetic field applies to the cooling and solidifying melt on the redistribution of components belonging to the classes of ferro-, para- and diamagnetic with a content of impurities, modifiers (up to 0.2 at.%) and alloying elements (up to 2.0 at.%), in the intermetallic phases of the Al-based alloy with Cu 1.9 at.% (3.7% wt.) and REM 3.1 at.% (13.7% wt.). The melt processing temperature is 820°C, the melt is cooled and solidified at $v$ = 10°C/s, under the influence of a magnetic field characterized by Hartmann number $Ha$ = 13.6. When obtaining the control alloy ($Ha$ = 0), in its structure inclusions are observed. They are: primary intermetallic compounds based on Al–Ti–REM, Al–REM–Cu, Al–Cu–REM, Al–REM–Cu–Fe and eutectics: one with coarse and thick long plates of a phase based on Al–REM–Cu, and the other with thin fine inclusions based on the Al–REM–Cu phase at $Ha$ = 0 and Al–Cu–REM at $Ha$ = 13.6. It is found, that magnetic field contributed to decrease in the size of the largest inclusions (Al–REM–Cu) and increase in the size of the smallest intermetallic compounds (Al–Ti–REM), distorted the faces of inclusions and plates of a coarse eutectic, and contributed to increase in the content of iron (ferromagnetic) in all phases by reducing the number of inclusions based on Al–REM–Cu–Fe. It is found, that when the concentration of para- and diamagnetic components in the alloy up to 0.2 at.%, a field influence on their content in the phase is determined by the value of the elements magnetic susceptibility. When the components concentration is up to 2.0 at.%, the field action also depends on the component concentration in the alloy. It is found, that in the structure of the alloy obtained by the conventional casting method under a weak magnetic field, changes took place, which are characteristic for the more expensive alloy treatments (high overheating of the melt, rapid solidification, heat treatment, modification, deformation). There is an intermetallic compounds grinding by 2–3 times, their loss of faceting in an amount up to 70–100%, inclusions destruction with sizes of more than 100 $\mu$m into fragments, a decrease in the amount of intermetallic compounds based on Al–REM–Cu–Fe up to 10 times, increasing in the concentration of most elements in eutectics, decreasing in the length of the coarse eutectic plates by 1.5 times and increasing in the proportion of fine eutectics by 5 times.