Many animal species exhibit food-anticipatory activity (FAA) when fed at a fixed time of the day. FAA exhibits properties of a daily rhythm controlled by food-entrainable circadian oscillators (FEOs). Lesion studies indicate that FEOs are separate from the light-entrainable circadian pacemaker (LEP) located in the suprachiasmatic nucleus. While anatomically distinct, food- and light-entrainable clocks do appear to interact, and the output of these clocks may be modulated by their phase relation. We report here an analysis of FAA in the BTBR T+ Itpr3tf/J (BTBR) mouse strain that provides new insights into the nature of interactions between food- and light-entrained clocks and rhythms. BTBR mice fed ad libitum exhibit an unusually short active phase and free-running circadian periodicity (~22.5 h). In a light-dark cycle, BTBR mice limited to a 4 h daily meal in the light period show robust FAA compared to the C57BL/6J mice. In constant darkness, BTBR mice exhibit clear and distinct free-running and food-anticipatory rhythms that interact in a phase-dependent fashion. The free-running rhythm exhibits phase advances when FAA occurs in the mid-to-late rest phase of the free run, and phase delays when FAA occurs in the late active phase. A phase-response curve (PRC) inferred from these shifts is similar to the PRC for activity-induced phase shifts in nocturnal rodents, suggesting that the effects of feeding schedules on the LEP in constant darkness are mediated by FAA. A phase-dependent effect of the free-running rhythm on FAA was evident in both its magnitude and duration; FAA counts were greatest when FAA occurred during the active phase of the free-running rhythm. The LEP inhibited FAA when FAA occurred at the end of the subjective day. These findings provide evidence for interactions between food- and light-entrainable circadian clocks and rhythms and demonstrate the utility of the BTBR mouse model in probing these interactions.