The suprachiasmatic nuclei (SCNs) control circadian rhythms of numerous behavioral and physiological responses. In hamsters, constant light causes "splitting" of circadian rhythms, such that a single daily bout of activity separates into two components, 12 h apart, with antiphase circadian oscillations in the left and right SCN. Given the phenotypic and functional heterogeneity of the SCN, in which ventrolateral but not dorsomedial neurons are retinorecipient, we asked how these two compartments respond to the constant lighting conditions that produce splitting, using three different phase markers of neuronal activity: PER1 (Period 1), c-FOS, and pERK (phosphorylated extracellular signal-regulated kinase). We report the emergence of a coherent novel network in which each side of the SCN exhibits two antiphase oscillating subregions, here termed "core-like" and "shell-like," in addition to the known antiphase oscillation between the right and left SCN. The novel SCN response entails a coherent rhythm in a core-like region of the SCN, which otherwise is not cycling. A mathematical model is presented, and this model interprets the observed changes in the proportion of in-phase and antiphase populations of SCN oscillators and suggests novel testable hypotheses. Finally, the functional significance of this network was explored by investigating the adjacent hypothalamus. Activation of the paraventricular nucleus is in-phase with the ipsilateral core-like SCN, whereas activation of the lateral subparaventricular zone is in-phase with the ipsilateral shell-like SCN, pointing to a multiplicity of SCN output signals. These results suggest a neural basis for internal coincidence of SCN oscillators, and a novel mechanism of plasticity in SCN neural networks and outputs.