The columnar composites obtained “in situ” through solidification of Al61Cu27Fe12 alloy by the Bridgman method were studied. It has been verified that the matrix consisted of cubic single crystal β phase and the reinforcement of icosahedral quasicrystal ψ phase and monoclinic crystal λ phase, which have the form of rods. This kind of composites will be named the Al-Cu-Fe crystal-quasicrystal (CQ) composites. The effect of heating from a temperature of about 100°C to about 650°C on the stress-strain relationships σ(ε) of parallel samples was studied. Additionally, the σ(ε) relationship was defined in cyclic load-unload tests at different temperatures. The composites were examined by powder X-ray diffraction and scanning electron microscope.