Hamsters will spontaneously ‘split’ and exhibit two rest–activity cycles each day when housed in constant light (LL). The suprachiasmatic nucleus (SCN) is the locus of a brain clock organizing circadian rhythmicity. In split hamsters, the right and left SCN oscillate 12 h out of phase with each other, and the twice-daily locomotor bouts alternately correspond to one or the other. This unique configuration of the circadian system is useful for investigation of SCN communication to efferent targets. To track phase and period in the SCN and its targets, we measured wheel-running and FOS expression in the brains of split and unsplit hamsters housed in LL or light–dark cycles. The amount and duration of activity before splitting were correlated with latency to split, suggesting behavioral feedback to circadian organization. LL induced a robust rhythm in the SCN core, regardless of splitting. The split hamsters’ SCN exhibited 24-h rhythms of FOS that cycled in antiphase between left and right sides and between core and shell subregions. In contrast, the medial preoptic area, paraventricular nucleus of the hypothalamus, dorsomedial hypothalamus and orexin-A neurons all exhibited 12-h rhythms of FOS expression, in-phase between hemispheres, with some detectable right–left differences in amplitude. Importantly, in all conditions studied, the onset of FOS expression in targets occurred at a common phase reference point of the SCN oscillation, suggesting that each SCN may signal these targets once daily. Finally, the transduction of 24-h SCN rhythms to 12-h extra-SCN rhythms indicates that each SCN signals both ipsilateral and contralateral targets.