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In addition to the well-known circadian rhythms in animal behavior, cell biology, and gene expression, there are also 12 hr rhythms. The mechanism giving rise to these 12 hr rhythms is not clear. We worked with the hypothesis that observed 12 hr rhythms in gene expression are the results of an interplay between components of the circadian clock. Analysis of mouse liver expression data indeed revealed a strong circadian component in observed 12 hr gene expression rhythms. We show theoretically that pairs of circadian transcription factors with certain circadian phase relationships can give rise to these 12 hr rhythms, if binding noncompetitively to the promoters of regulated genes. We took an inventory of circadian transcription factors in mouse liver using available microarray data and matched these to predicted binding sites in the promoters of genes displaying 12 hr rhythms. Binding sites for transcription factor pairs with phase relationships predicted by theory were overrepresented in these promoters.