In the systems Ba/Mg/(Si, Ge), two new ternary Zintl phases with the compositions BaMg4Si3 and BaMg4Ge3 were found and structurally characterized Both compounds are isotypic and crystallize with a new structure type [BaMg4Si3, P4/mmm, Z = 1, a = 4.6115(9) Angstrom, c = 8.615(2) Angstrom; BaMg4Ge3, P4/mmm, Z = 1, a 4.6335(8) Angstrom, 8.746(?) Angstrom]. The anionic partial structure is built of X-2(6-) dumbbells and isolated X4- ions (X = Si, Ge), and the structure can be described according to the Zintl-Klemm-Busmann concept with the formulation (Ba2+)(Mg2+)(4)[X-2(6-)] [X4-]. The BaMg4X3 structure can also be described as a result of the fusion of the structures of Mg2X and BaMg2X2. In this regard, BaMg4Si3 and BaMg4Ge3 are very striking examples of chemical twinning.