Phase relations in the pseudo-binary systems RFeO3-R2Ti2O7 (R: Lu, Ho and Dy), RGaO3-R2Ti2O7 (R: Lu and Er), LuAlO3-Lu2Ti2O7 and RAO3-R2Ti2O7 (R: Lu and Yb. A: Cr and Mn) at elevated temperatures in air were determined by means of a classic quenching method. There exist Lu(Fe1−xTix)O3+x/2, R(Ga1−xTix)O3+x/2 (R: Lu and Er) and Lu(Al1−xTix)O3+x/2 (2/3≤ x≤3/4) having the Yb(Fe1−xTix)O3+x/2-type of crystal structure (x=0.72, space group: R3m, a(Å)=17.9773 and c(Å)=16.978 as a hexagonal setting) in these pseudo binary systems. Eighteen compounds R(A1−xTix)O3+x/2 (R: Lu-Sm and Y, A: Fe, Ga and Al) were newly synthesized and their lattice constants as a hexagonal setting were measured by means of the X-ray powder diffraction method. The R occupies the octahedral site and both A and Ti does the trigonalbipyramidal one in these compounds. Relation between lattice constants for the rhombic R(A1−xTix)O3+x/2 and the monoclinic In(A1−xTix)O3+x/2 are as follows, ah≈5 x bm, ch≈3 x cm x sin β and am=31/2 x bm, where ah and ch are the lattice constants as a hexagonal setting for R(A1−xTix)O3+x/2 and am, bm, cm and β are those of the monoclinic In(A1−xTix)O3+x/2. Crystal structural relationships among α-InGaO3 (hexagonal, high pressure form, space group: P63/mmc), InGaO3 (rhombic, hypothetical), (RAO3)n(BO)m and RAO3(ZnO)m (R: Lu-Ho, Y and In, A: Fe, Ga, and Al, B: divalent cation element, m, n: natural number), the orthorhombic-and monoclinic In(A1−xTix)O3+x/2 (A: Fe, Ga, Al, Cr and Mn) and the hexagonal-and rhombic R(A1−xTix)O3+x/2 (R: Lu-Sm and Y, A: Fe, Ga and Al) are schematically presented. We concluded that the crystal structures of both the α-InGaO3 (high pressure form, hexagonal, space group: P63/mmc) and the hypothetical InGaO3 (rhombic) are the key structures for constructing the crystal structures of these compounds having the cations with CN=5.