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The purpose of this study was to determine whether the chemical compositions of Alnico alloys had any effects on the electrical discharge machining (EDM) performance and the surface finish. This article compares the behavior of three different Alnico alloys in electrical discharge machining. The experiments were conducted under different conditions using a BP93L EDM machine (ZAP BP, Końskie, Poland), applying an additional rotary motion to the electrode. A Box–Behnken experimental design was employed to analyze the influence of three factors, i.e., the spark current, the pulse-on time, and the pulse-off time, at three levels for three Alnico alloys. The material removal rate (MRR) was calculated for the different process parameters. After the EDM, the surface roughness was studied using a Talysurf CCI Lite non-contact profiler (Taylor–Hobson, Leicester, UK). The next step of the experiments involved preparing metallographic specimens to be observed by means of scanning electron microscopy (SEM) and optical microscopy (OM). Measurements of the nanohardness were also performed. The experimental data were then analyzed using Statistica software version 10 (64-bit) to determine and graphically represent the relationships between the input and output parameters for the three Alnico alloys. The chemical compositions of the Alnico alloys affected the thickness of the white layer (higher cobalt content, lower white layer thickness) and the material removal rate. The higher the cobalt content, the thinner the white layer and the lower the material removal efficiency. Moreover, the cobalt content in Alnico alloys influenced the shape of the precipitates; these ranged from spheroidal (13% Co) to mix-shaped (21.3% Co) to flake-shaped (32.2%). The hardness of the resulting white layer was 874 HV at10 mN. [ABSTRACT FROM AUTHOR]