The algal flagellate Euglena grown photoautotrophically in L:D 3:3 displays a circadian rhythm of cell division. Oscillatory models for cell cycle (CDC) control (particularly those of the limit cycle variety) include the property of phase perturbation, or resetting. This prediction has been tested in synchronous cultures in which the free-running rhythm has been scanned by 3-hr light signals. A strong (Type 0) phase response curve (PRC), yielding both advances and delays as great as 15 hr, has been derived. A second prediction of the limit cycle model is that there exists a pulse of a critical intensity, which, if given at one specific phase of the rhythm (the singularity point), should result in a phaseless, motionless state in which the rhythmicity disappears. Such a point has been found in Euglena in the late subjective night for light pulses having an intensity ranging from 40 to 700 lx. Finally, circadian oscillators typically display temperature-compensated period lengths within the physiological range of steady-state temperatures, although the length of the CDC is commonly thought to be highly temperature dependent. We have found that over a range of at least 10 degrees C, the period of the division rhythm is only slightly affected, exhibiting a Q10 of about 1.05-1.20. These observations, therefore, collectively implicate a circadian oscillator in the control of the CDC.