Two new intermetallic compounds, Yb(2)Ga(4)Ge(6) and Yb(3)Ga(4)Ge(6), were obtained from reactions in molten Ga. A third compound, Eu(3)Ga(4)Ge(6), was produced by direct combination of the elements. The crystal structures of these compounds were studied by single-crystal X-ray diffraction. Yb(2)Ga(4)Ge(6) crystallizes in an orthorhombic cell with a=4.1698(7), b=23.254(4), c=10.7299(18) A in the polar space group Cmc2(1). The structure of RE(3)Ga(4)Ge(6) is monoclinic, space group C2/m, with cell parameters a=23.941(6), b=4.1928(11), c=10.918(3) A, beta=91.426(4) degrees for RE=Yb, and a=24.136(2), b=4.3118(4), c=11.017(1) A, beta=91.683(2) degrees for RE=Eu. The refinement [I>2 sigma(I)] converged to the final residuals R(1)/wR(2)=0.0229/0.0589, 0.0411/0.1114, and 0.0342/0.0786 for Yb(2)Ga(4)Ge(6), Yb(3)Ga(4)Ge(6), and Eu(3)Ga(4)Ge(6), respectively. The structures of these two families of compounds can be described by a Zintl concept of bonding, in which the three-dimensional [Ga(4)Ge(6)](n-) framework serves as a host and electron sink for the electropositive RE atoms. The structural relation of RE(3)Ga(4)Ge(6) to of Yb(2)Ga(4)Ge(6) lies in a monoclinic distortion of the orthorhombic cell of Yb(2)Ga(4)Ge(6) and reduction of the [Ga(4)Ge(6)] network by two electrons per formula unit. The results of theoretical calculations of the electronic structure, electrical transport data, and thermochemical and magnetic measurements are also reported.