This paper reveals potential micro mechanisms underlying time-dependent anelasticity observed in Al-(1 wt%)Cu thin films. The analyzed deformation mechanisms involve dislocation motion and interaction with solute diffusion, grain boundaries and precipitates. In order to investigate the role of these mechanisms, Al-(1 wt%)Cu alloy thin films are heat treated to systematically change the precipitation state, while characterizing the grain boundary distribution with electron backscatter diffraction. Micromechanical characterization is performed by microbeam bending, nano-tensile creep testing and nano-indentation. Results in microbeam bending reveal, for all precipitate and grain boundary states considered, a similar time-dependent evolution of the anelastic strain after load release. The magnitude of the recovered strain is also observed to be independent of the precipitate or grain boundary configuration. The nano-tensile creep test also indicates the same time-dependent anelastic evolution, indicating that the loading state does not affect the underlying mechanisms. Analysis of strain bursts in nano-indentation shows that pinning of dislocations by Cu solutes is unaffected by the precipitation state. Based on uniaxial creep and time-dependent anelasticity measurements in pure Al specimens, it is made plausible that the time-dependent anelasticity originates from diffusion-limited glide or climb of dislocation segments that are pinned at Cu solutes or in dislocation structures, which provide an internal driving force.