Mechanical spectroscopy measurements were performed on two types of materials: decagonal quasicrystalline Al-Cu-Fe-Cr coatings deposited on a mild steel substrate and aluminium or magnesium matrix composites reinforced with icosahedral quasicrystalline Al-Cu-Fe particles. The internal friction spectra of the substrate with three different thicknesses of the coating indicate that the internal friction of such composites is mostly caused by the quasicrystalline coating and that the contributions of the steel substrate and of the interface are small. The shear modulus measured in torsion increases with temperature, while the Young's modulus measured in flexion behaves normally. This shear modulus anomaly is interpreted as due to a solid friction between cracked segments of the quasicrystalline coating. This phenomenon can also explain the broad athermal maximum, which was found to occur in isochronal internal friction measurements. A quantitative model successfully reproducing the observed behaviour was developed. Finally, the reversible high-temperature exponential background was interpreted as due to the onset of the brittle-to-ductile transition, which may be associated with dislocation motion controlled by collective phason flips in the quasicrystalline coating. The measured activation enthalpy is similar to the value that was deduced from compression tests performed on icosahedral Al-Cu-Fe bulk material. Aluminium or magnesium matrix composites reinforced with icosahedral Al-Cu-Fe particles were processed by gas pressure infiltration and characterised by X-ray diffractometry, electron microscopy observations, micro-hardness measurements, and compression tests. The internal friction spectra of these composites also show a high-temperature exponential background, while measurements of the matrix alone or of the matrix with Al2O3 short fibres exhibit a different behaviour. The difference can be explained by a partial phase transformation of the matrix due to the presence of the quasicrystalline particles. The exponential background is probably caused by dislocation motion in the matrix, however, the effect of the quasicrystalline reinforcement can be neither excluded nor confirmed with certainty.