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The Al3Cu4 composition, with an e/a ratio of 1.86 being close to ternary Al-Cu-TM (Transition Metal) quasicrystals, has been chosen for the search of AI-Cu approximants. Phase structures and compositions were studied using TEM, ii-ray diffraction and EPMA techniques. Two new phases were found: face-centered orthorhombic oF-Al43.2Cu56.8 (a = 0.816(6), b = 1.414(9), c = 0.999(5) nm) and body-centered orthorhombic oI-Al41.3Cu58.7 (oI, a = 0.408(3), b = 0.707(4), c = 0.999(5) nm). Their e/a ratios are the same as that of the Al-Cu-Fe icosahedral quasicrystal. Their space groups are probably oF-Fmm2 and oI-Imm2. Both are B2 vacancy-containing superstructures; unit cell compositions can be expressed approximately as oF-Al(36)Cu(48)square(12) and oI-Al(8)Cu(12)square(4) (square: vacancies). They both exist in twinning variants of the types 120 degrees/[001] and 180 degrees/[310]. Such twinning modes indicate that these orthorhombic phases are the decomposition products of a high-temperature parent phase epsilon 2-Al2Cu3, the atomic structure of which contains pentagonal atomic arrangements. Therefore the of, oI, and epsilon 2 phases are all B2-based approximants corresponding to the Al-Cu-TM quasicrystals.