The structures of alpha-Ba(3)RAl(2)O(7.5) and beta-Ba(3)RM(2)O(7.5) complex oxides (R = rare-earth elements, M = Al, Ga) have been studied by a combination of X-ray diffraction, electron diffraction (ED) and high-resolution electron microscopy (HREM). The alpha and beta forms have cell parameters related to the perovskite subcell: a = 2a(per), b = a(per)(2)(1/2), c = 3a(per)(2)(1/2), however, the alpha form has an ortho-rhombic unit cell whereas the beta form adopts monoclinic symmetry. The crystal structure of monoclinic Ba(3)ErGa(2)O(7.5) was refined from X-ray powder data (space group P2/c, a = 7.93617(9), b = 5.96390(7), c = 18.4416(2) Å, beta = 91.325(1) degrees, R(I) = 0.023, R(P) = 0.053), the structure of the alpha form (space group Cmc2(1)) was deduced from ED and HREM data. The important feature of the alpha and beta structures is the presence of slabs containing strings of vertex-sharing tetrahedral Al(2)O(7) pairs. Two almost equivalent oxygen positions within the strings can be occupied either in an ordered manner leading to the low-temperature beta phase or randomly resulting in the high-temperature alpha structure. The critical temperature of this order-disorder phase transition was determined by high-temperature X-ray diffraction and by differential thermal analysis (DTA). In situ ED and HREM observations of the second-order phase transition confirmed the symmetry changes and revealed numerous defects (twins and antiphase boundaries) formed during the phase transformation.