The whole isothermal section of the La-Ag-Mg phase diagram at 400 degrees C was constructed by means of phase identification and analysis on about eighty annealed ternary alloys. The tendency of Ag and Mg to reciprocally substitute in binary Ag-Mg phases reflects in the formation of several La-Ag-Mg ternary phases including solid solutions based on boundary binary phases, which show wide homogeneity regions extending at a constant La-content. Among the solid solutions, La(AgxMg1-x) (0 <= x <= 1, cP2-CsCl), La(AgxMg1-x)(3) (0 <= x <= 0.67, cF16-BiF3) and La-2(AgxMg1-x)(17) (0 <= x <= 0.30, hP42-3.64-CeMg10.3) are the most extended. The crystal structure of La2(AgxMg1-x)17 was determined from X-ray diffraction data refinement on two single crystals corresponding to x = 0 and x approximate to 0.2: a hexagonal disordered structure based on the CeMg10.3 type structure is proposed for this solid solution (for La2Mg17: P6(3)/mmc, hP42-3.64, a = 1.0387(1), c = 1.0263(2) nm, wR(2) = 0.0727, 408 F-2 values, 29 variables). Among the ternary compounds, the crystal structures of tau(1)-LaAg1+xMg1-x (0 <= x <= 0.15, hP9-ZrNiAl), tau(2)-La4Ag10+xMg3-x (-0.15 <= x <= 0.3, oS68-Ca4Au10In3) and tau(5)-La4Ag10.3+xMg12-x (-0.4 <= x <= 0.70, oS116 -10.33-La4Ag10.3Mg12) were confirmed and their homogeneity ranges established. The crystal structures of tau(4)-LaAg4+xMg2-x (-0.15 <= x <= 0.88, tI14-YbAl4Mo2), tau(4)'-LaAg5+xMg1-x (-0.1 <= x <= 0.05, tP14-LaAg5Mg) and tau(6)-La3Ag4+xMg12-x (-1.6 <= x <= 1.0, hP38-Gd3Ru4Al12) were solved and refined by X-ray powder diffraction data analysis. The phases tau(4) and tau(4)' crystallize in two strictly correlated tetragonal structures, body centered and primitive respectively: these two structures were interpreted as structural modifications of the same phase. Two more new ternary phases, tau(3)-LaAg2+xMg2-x (0 <= x <= 0.45, oS20-LaAg2Mg2) and tau(7)-La(AgxMg1-x)(12) (0.11 <= x <= 0.21, tI208-La(AgxMg1-x)(12)), were also detected in this system. (C) 2011 Elsevier Ltd. All rights reserved.