Rare-earth metal aluminum germanides with the general formula REAl1-xGe2 (RE = Gd, Tb, Dy, Ho, Er, Tm, Lu, and Y) have been synthesized by direct fusion of the corresponding elements. The structures have been studied by single-crystal X-ray diffraction and selected-area electron diffraction (SAED). The average structure represents a randomly stuffed variant of the orthorhombic ZrSi2 structure type, also known as the CeNi1-xSi2 type (Pearson symbol oC16; space group Cmcm). The SAED patterns for selected members of the family suggest the coexistence of commensurate and incommensurate structural modulations. The most prominent model for long-range vacancy ordering is the Tb4FeGe8 type (Pearson symbol mP26; space group P2(1)/n), which is the commensurate 4-fold superstructure of CeNi1-xSi2 (x = 3/4). Short-range correlations cause additional deviations in the 4-fold superlattice. These results shed more light on the structural complexity as a function of the aluminum vacancies and size of the rare-earth metal. Magnetic susceptibility measurements are presented and discussed. The measured ordering temperatures and calculated ones based on empirical rules and Ruderman-Kittel-Kasuya-Yosida interactions are shown to be in close agreement.