F-actin bundles are prominent cytoskeletal structures in eukaryotes. They provide mechanical stability in stereocilia, microvilli, filopodia, stress fibers and the sperm acrosome. Bundles are typically stabilized by a wide range of specific crosslinking proteins, most of which exhibit off-rates on the order of 1s(-1). Yet F-actin bundles exhibit structural and mechanical integrity on time scales that are orders of magnitude longer. By applying large deformations to reconstituted F-actin bundles using optical tweezers, we provide direct evidence of their differential mechanical response in vitro: bundles exhibit fully reversible, elastic response on short time scales and irreversible, elasto-plastic response on time scales that are long compared to the characteristic crosslink dissociation time. Our measurements show a broad range of characteristic relaxation times for reconstituted F-actin bundles. This can be reconciled by considering that bundle relaxation behavior is also modulated by the number of filaments, crosslinking type and occupation number as well as the consideration of defects due to filament ends.