The isothermal section of the La-Co-Mg system at 400 °C was determined by characterization of about thirty ternary alloys synthesised by induction melting in sealed Ta crucibles and then annealed. Scanning electron microscopy (SEM) coupled with energy dispersive x-ray spectroscopy (EDXS) and x-ray powder diffraction (XRPD) were used to analyze microstructures, identify phases, measure their compositions and determine their crystal structures. Phase equilibria are characterized by the absence of ternary solid solutions and by the presence of three ternary phases. The existence and the crystal structure of the La4-xCoMg1 + x (τ1, 0 ≤ x ≤0.15, cF96-Gd4RhIn) were confirmed and its homogeneity region determined; the new phases La23-xCo7Mg4 + x (τ2, -0.50≤ x ≤0.60, hP68-Pr23Ir7Mg4) and ~La38Co55Mg7 (τ3, unknown crystal structure) were detected
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