Reported are the synthesis and the structural characterization of two members of a new homologous series of polar intermetallic compounds, which exist only with mixed alkaline-earth and rare-earth metal cations. Crystals of (Eu1-xCax)(4)In3Ge4 (0.35(1) <= x <= 0.70(1)) and (Eu1-xCax)(3)In2Ge3 (0.78(1)<= x <= 0.90(1)) have been grown using a molten In metal flux and structurally characterized by single-crystal X-ray diffraction. (Eu1-xCax)(4)In3Ge4 adopts the monoclinic Mg5Si6-type structure (space group C2/m, Z = 2, Pearson symbol mS22) with lattice parameters a = 16.874(1)-17.024(2) angstrom, b= 4.496(3)-4.556(1) angstrom, c= 7.473(4)-7.540(1) angstrom, and beta = 107.306(10)-105.631(3)degrees. (Eu1-xCax)(3)In2Ge3 crystallizes with a novel orthorhombic structure (space group Pnma, Z=4, Pearson symbol oP32) with lattice parameters in the ranges a = 7.382(2)-7.4010(9) angstrom, b = 4.452(1)-4.4640(6) angstrom, and c = 23.684(6)-23.734(3) angstrom, depending on the Eu/Ca ratio. The polyanionic substructures in both cases are related and are based on InGe4 edge-shared tetrahedra, Ge-2 dimers, and bridging In atoms in a nearly square-planar environment. The (Eu1-xCax)(4)In3Ge4 structure can be viewed as a 1:1 intergrowth of Mo2FeB2-like and TiNiSi-like fragments, whereas (Eu1-xCax)(3)In2Ge3 can be rationalized as a 2:1 intergrowth of the same structural motifs. Both phases exhibit fairly wide homogeneity ranges and exist only with mixed cations. The experimental results have been complemented by linear muff in-tin orbital tight-binding band structure calculations, as well as an analysis of the observed cationic site preferences.