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Two types of icosahedral quasicrystals are observed in Al65Cu20Fe15−xCrx (0 ≦ x ≦ 15) alloys, the face‐centred AlCuFe‐type icosahedral phase with dissoluted Cr and the primitive AlCuCr‐type icosahedral phase with dissoluted Fe. In the vicinity of Al65Cu20Fe8Cr7 a stable decagonal phase (a = 0.45 nm and c = 1.23 nm) forms competitively with the icosahedral quasicrystals. All these three quasicrystalline phases can be regarded as Hume‐Rothery phases stabilized by the energy band factor. The density is measured to be 4.57, 4.44, and 4.11 g/cm3 for the icosahedral Al65Cu20Fe15, the decagonal Al65Cu20Fe8Cr7, and the icosahedral Al65Cu20Cr15 alloys, respectively. Depending on the composition in the range between Al65Cu20Fe8Cr7, and Al65Cu20Cr15, several crystalline phases are observed during the transformation of the AlCuCr‐type icosahedral phase: the 1/1 –3/2‐type orthorhombic (0) and the 1/0 ‐ 3/2‐type tetragonal (t) approximants of the decagonal phase, a hexagonal (h) phase, as well as a long‐range vacancy ordered τ3‐phase derived from a CsCI‐type structure with a = 0.2923 nm. The structures of all the crystalline phases are closely related to those of the icosahedral (i) and decagonal (d) quasicrystals, which leads to a definite orientation relationship as follows: i5 ∥ d10 ∥ o[100] ∥ t[100] ∥ h[001] ∥ τ3[110].

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