Although chronobiologists have postulated self-sustainability in circadian clocks, we report here two examples of damped oscillation in the cyanobacterial circadian system. First, low temperature transformed the self-sustained KaiC phosphorylation rhythm into damped oscillations. Second, deletion of the kaiA gene showed damped oscillation in the bioluminescent rhythm. These damped rhythms resonated with periodical environmental changes and then recovered their oscillation amplitudes. Numerical experiments confirmed that biochemical networks with the characteristic of self-sustained oscillation are rare. Evolutionary searches revealed that photoperiodism might contribute to evolving the self-sustainability of circadian rhythms. Although damped oscillators have not received substantial chronobiological analyses, our findings suggest that the circadian clock can easily transform into a damped oscillator by environmental or genetic perturbation and might function as a semi-clock system.