The crystal structures of Ca(Al0.5Si0.5)O-2.75 and Ca(Al0.4Si0.6)O-2.8 ordered oxygen-deficient perovskite phases are synthesized at 7 and 11 GPa, respectively, and 1500 A degrees C, and were studied using NMR and synchrotron powder X-ray diffraction. Si-29 MAS NMR, Al-27 MAS and 3Q MAS NMR measurements revealed a single tetrahedral Si and single octahedral Al peak for the Ca(Al0.5Si0.5)O-2.75 phase, and a tetrahedral and an octahedral Si peak and a single octahedral Al peak for the Ca(Al0.4Si0.6)O-2.8 phase. Using this structural information as constraints, the crystal structures were solved from synchrotron X-ray diffraction data by the structure determination from powder diffraction (SDPD) technique. To double-check the structures, first-principles calculations of NMR parameters (chemical shifts and electric field gradients) were also conducted after relaxing the obtained structures. The calculated NMR parameters of both phases are consistent with the observed NMR spectra. The crystal structures of both phases consist of a perovskite-like layer of (Al,Si)O-6 octahedra and a double-layer of SiO4 tetrahedra that are stacked alternatively in the [111] direction of ideal cubic perovskite. The perovskite-like layer is made of a double-layer of Al octahedra for the Ca(Al0.5Si0.5)O-2.75 phase, and a triple-layer with a Si octahedral layer sandwiched between two Al octahedral layers for the Ca(Al0.4Si0.6)O-2.8 phase. A unique feature common to both structures is that each SiO4 tetrahedron has one terminal oxygen that is not shared by other Si or Al. Homologous relation among these phases and merwinite (Ca3MgSi2O8) in terms of different numbers (1-3) of octahedral layers within the perovskite-like layer is noted.