In order to eliminate internal and surface defects, which appear in the ingots during continuous casting of metallic alloys, homogeneous and fine structures are often required. Therefore, when the adjunction of inoculant substances is not possible, the electromagnetic stirring (EMS) process is used during solidification. It consists to create convective mouvements in the liquid part of the casting, by the action of an electromagnetic field. A fine equiaxed grain structure can then be observed. The main goal of this research is to study the effect of the EMS process on grain structures for two industrial copper-base alloys : C97 (Cu-1%Ni-1%Pb-0.2%P) and BZ4 (Cu-4%Zn- 4%Sn-4%Pb). In particular, it included the determination of the optimal experimental parameters to obtain a grain refinement, the characterization of their effect on the solidification and the understanding of the physical mechanisms driving grain refinement. For that purpose, a Bridgman type furnace was modified in order to add an electromagnetic stirring device. Indeed, as the industrial continuous casting process is rigid and complex, the investigations were easier to carry out on the Bridgman installation, enabling us to define the influence of each experimental parameter : power of the induction, casting speed, coil position, temperature of the liquid and composition of the alloy. This experimental study was completed by the numerical simulation of the experimental conditions. The analysis of the structures, refined or not, showed that the dominant factors concerning the capacity of EMS to refine the structure, are the position of the inductor with respect to the liquidus, and the permeability of the mushy zone of the alloy. The more permeable the alloy is near the liquidus the more effective is the grain refinement. Concerning the position of the inductor, in-situ temperature measurements clearly revealed the local reheating of the liquid induced by convection. To correctly refine the low concentration alloy (C97), this local reheating must be brought on the position close to the dendrite position. During EMS-induced grain refinement, fragmentation of the dendrite arms by remelting and their survival in the melt are prevalent. Remelting can occur only if the "hot" liquid penetrates the mushy zone. Thus, the concept of permeability according to the model of Karman-Cozeny was used in simulation in order to characterize the penetration of the liquid in the mushy zone. From these results, a criterion of remelting, based on Flemings model of macrosegregation, was adapted and applied to our case. This criterion shows that remelting takes place if the velocity of the interdendritic liquid is lager than the speed of the isotherms. The velocity of the interdendritic liquid was calculated by numerical simulation for both alloys, under various experimental conditions. These results confirmed the importance to bring the inductor closer to the position of the liquidus to remelt dendrites, in particular in the case of the C97 alloy, which proves to be much more difficult to refine than the BZ4 alloy. Lastly, survival of the fragments was also studied. It depends on the casting conditions (casting speed and thermal gradient) and on the composition of the alloy. From the differences in composition of both alloys, it could be shown that the survival of dendrites fragments is improved during the solidification of the BZ4 alloy, compared with the C97 alloy.