Peculiarities of the interaction of the components in the systems Eu-Mg-Al, {Y,Gd,Tb}-Ge-Al, {Sm,Gd,Tb}-Co-Al, {Y,Gd-Lu}-Ni-Al, {Sm,Tb}-Pd-Al, Sm-Os-Al, {Gd,Tb}-Ir-Al and {Sm,Gd,Tb}-Pt-Al in the Al-rich region were established based on phase analysis of 120 alloys using X-ray diffraction (XRD) and energy dispersive X-ray analysis (EDX). 27 new ternary aluminides were synthesized and their crystal structures were determined by means of single-crystal and powder diffraction. Five new structure types were discovered: Tb2Ge3Al3, Yb0.67Ni2Al6, Dy4Ni9Al24, Tb0.67PdAl3, Sm2Os3Al15. Stacking rules for close-packed layers of composition R0.67Al, T and Al in aluminides with d(T)- and f(R)-elements were formulated, which may help to predict new structures. A homologous series of structures with the general formula R0.67TnAl2n+m, containing slabs of composition R0.67Al, TAl2 and Al, was deduced; a hypothetical structure R2T6Al15 with fully ordered distribution of R atoms and Al3 triangles was derived, which was later experimentally verified by another scientific group. The structure of the compound Tb2Ge3Al3 is built of layers similar to those observed in aluminides with d- and f-elements, but contains in addition a different kind of layer: close-packed layers of R atoms. The structure can also be described as an intergrowth of CaAl2Si2- and ScAuSi-type slabs. The phase equilibria in the system Tb-Ge-Al at 600, 650 and 800°С in the region >= 33.3 at.% Al were established by means of XRD, EDX, and differential thermal analysis (DTA). The alumogerminide Tb2Ge3Al3 was found to exist in a narrow temperature range, 618-748°С. Above 748°C it decomposes into Tb2Ge4Al3, TbGeAl and Al, whereas below 618°C a three-phase equilibrium, TbGe2Al2 + TbGeAl + Al, was observed in this region. The isotypic compound Y2Ge3Al3 was found to exist in the range 620-782°С. The structures of the R2-xT3Al15+2x aluminides contain a framework of [TAl10R2] icosahedra; the remaining R atoms (in part replaced by Al atoms) are distributed in hexagonal channels along the 6-fold axes in a partly disordered manner. The occupancies of the split sites were checked to be in agreement with the average interatomic distance between the sites. The ternary aluminides R0.67Ni2Al6 with R = Tb, Er and Tm were found to be Curie-Weiss paramagnets; Lu0.67Ni2Al6 is also paramagnetic, whereas the compound with Yb is a dense Kondo system. The compounds R0.67Ni2Al6 (R = Tb, Er-Lu) are characterized by metallic type conductivity.