Many eukaryotic unicells exhibit endogenous periodicities, in a broad range of frequencies. Euglena gracilis, e.g. is capable of producing rhythms of ca. 8 min, 1 h, 1.5 h, 4.5 h and 1 d, several of them stimultaneously. Tetrahymena thermophila can switch between ultradian and circadian periodicities. In both species, ultradian and circadian rhythms share the phenomenon of temperature compensation. The multiplicity of rhythms with similar properties, as generated at the cellular level, is discussed to reflect the behaviour of a multidimensional attractor. The cellular circadian oscillator can enter an aperiodic state: in Euglena upon exposure to series of short light pulses of extremely low zeitgeber strength, which have to be given, however, in a sufficiently high frequency; in the dinoflagellate Gonyaulax polyedra by exposure to low temperature. Transitions between periodic and aperiodic states can be used for analysing cellular oscillatory elements. In Gonyaulax, low temperature desensitizes the oscillator to phase shifting by 80 S translational inhibitors. A lowered temperature which is still permissive for periodic behaviour makes Gonyaulax responsive to short-days, which induce formation of asexual cysts. Encystment can be also provoked by several biogenic amines, in particular 5-methoxylated indoleamines. Melatonin and 5-methoxytrptamine exist in Gonyaulax  in high concentrations and show circadian rhythms with nocturnal maxima. In this dinoflagellate, melatonin may mediate the information of darkness, as in vertebrates. Cyst-inducing amines stimulate bioluminescence and seem to trigger encystment by lowering intracellular pH. Sensitivity of cells to these agents varies in a circadian fashion. Melatonin is readily degraded by light-induced superoxide anions. Cell protection by scavenging of these radicals may have been the original function of melatonin; a resulting cycle in concentration due to lesser nocturnal destruction may have given rise for utilizing this indoleamine as an indicator of darkness.