Circadian clocks temporally organize physiology and behavior of organisms exposed to the daily changes of light and temperature on our planet, thereby contributing to fitness and health. Circadian clocks and the biological rhythms they control are characterized by three properties. (1) The rhythms are self-sustained in constant conditions with a period of ~ 24 hr,(2), they can be synchronized to the environmental cycles of light and temperature, and (3), they are temperature compensated, meaning they run with the same speed at different temperatures within the physiological range of the organism. Apart from the central clocks located in or near the brain, which regulate the daily activity rhythms of animals, the so-called peripheral clocks are dispersed throughout the body of insects and vertebrates. Based on the three defining properties, it has been difficult to determine if these peripheral clocks are true circadian clocks. We used a set of clock gene -luciferase reporter genes to address this question in Drosophila circadian clocks. We show that self-sustained fly peripheral oscillators over compensate temperature changes, i.e., they slow down with increasing temperature.This over-compensation is not observed in central clock neurons in the fly brain, both in intact flies and in cultured brains, suggesting that neural network properties contribute to temperature compensation. However, an important neuropeptide for synchronizing the circadian neuronal network, the Pigment Dispersing Factor (PDF), is not required for selfsustained and temperature-compensated oscillations in subsets of the central clock neurons.Our findings reveal a fundamental difference between central and peripheral clocks, which likely also applies for vertebrate clocks.