Processes as diffusion, plastic deformation, and creep in quasicrystals are expected to be mediated by lattice defects as vacancies and phasons. The aim of the present study is to investigate to which extent techniques as positron annihilation spectroscopy [1, 2] can be utilized to detect and analyse vacancies. Investigations of other systems like intermetallic compounds (FeAl, NiAl, TiAl) showed that positron lifetime spectroscopy is a specific tool for gaining information on the migration and the formation of thermal defects [3, 4]. The research work presented here will focus on the investigation of icosahedral AlPdMn quasicrystals. In addition, structural vacancies in quasicrystalline icosahedral Zn(61)Mg(28)Ho(11) and decagonal Al(72)Ni(20)Co(8) are studied. Furthermore, we report on slow equilibration processes of thermal atomic defects in AIPdMn after fast temperature changes studied by time-differential high-resolution dilatometry [7].