Circadian (similar to 24 hour) clocks are fundamentally important for coordinated physiology in organisms as diverse as cyanobacteria and humans. All current models of the molecular circadian clockwork in eukaryotic cells are based on transcription-translation feedback loops. Non-transcriptional mechanisms in the clockwork have been difficult to study in mammalian systems. We circumvented these problems by developing novel assays using human red blood cells, which have no nucleus (or DNA) and therefore cannot perform transcription. Our results show that transcription is not required for circadian oscillations in humans, and that non-transcriptional events seem to be sufficient to sustain cellular circadian rhythms. Using red blood cells, we found that peroxiredoxins, highly conserved antioxidant proteins, undergo similar to 24-hour redox cycles, which persist for many days under constant conditions (that is, in the absence of external cues). Moreover, these rhythms are entrainable (that is, tunable by environmental stimuli) and temperature-compensated, both key features of circadian rhythms. We anticipate that our findings will facilitate more sophisticated cellular clock models, highlighting the interdependency of transcriptional and non-transcriptional oscillations in potentially all eukaryotic cells.