Circadian rhythms, biological timing processes with a period of ~24 h, are dynamic phenomena containing feedback loops, and then it has been of interest to apply mathematical methods to the circadian studies. Cyanobacteria are the simplest organisms known to exhibit circadian rhythms, which gives a model to understand the structural basis of the stable rhythmicity physiologically and genetically. In Synechococcus, kaiA, kaiB and kaiC genes have been characterized as essential clock regulators. Among three kai transcripts, KaiC plays a central role and exhibits rhythms both in expression and phosphorylation status, and regulates its own expression negatively as well as positively. This switching feedback regulation of KaiC seems to depend on KaiC's phosphorylation status, however, the precise mechanism is still unknown. Moreover, it has been reported that KaiC forms complex with KaiA and KaiB, and the concentration of the complex oscillates in circadian period. Using mathematical model, we investigate how KaiC regulates its expression and how phosphorylation and complex formation contribute to the regulation system. We started from the simplest model, three-variable model (kaiBC mRNA, non-phosphorylated KaiC and phosphorylated KaiC). In this model, we assumed that transcription of kaiBC switches depending on the concentrations of non-phosphorylated KaiC and (or) phosphorylated KaiC. Taking account of all possible switching patterns, we examined which pattern can generate oscillation. Interestingly, the mathematical analysis showed that only two patterns can generate oscillation, (1) Negative Feedback by phosphorylated KaiC, (2) Positive Feedback by phosphorylated KaiC. In either case, non-phosphorylated KaiC can merely affect its transcription. As for the structure, the pattern (1) corresponds to the earliest model for circadian clocks. On the other hand, it should be noted that the pattern (2) is regulated by positive feedback, which is repressed by KaiC dephosphorylation as indirect negative feedback. These results are dynamically rigorous, however, the computer simulation showed that neither of these patterns reproduce all the observed behavior of kaiBC, which means that difference in phosphorylation level only can not explain the transcriptional oscillation. It also implied complex formation may indispensable to understand cyanobacterial circadian rhythms. We will report the upcoming result by a five-variable model (kaiBC, non-phosphorylated KaiC, phosphorylated KaiC, 1st complex and 2nd complex).