Several experimental studies have altered the natural phase relationship between photic and non-photic zeitgebers, in order to assess their hierarchy in the entrainment of circadian rhythms. In order to interpret the complex results that emerge from these conflicting zeitgeber protocols, we present computer simulations of two coupled oscillator systems forced by two independent zeitgebers. First proposed in 1959 by Pittendrigh and Bruce to model results of their studies on the light and temperature entrainment of eclosion in Drosophila, such a circadian system is also coherent with recent data from many organisms. Our simulations show how the phase of a circadian rhythm varies with a systematic change of the phase relationship between two zeitgebers. "Phase-jumps" and hysteresis in the overt rhythm are shown to arise if the inter-oscillator coupling is high in relation to the zeitgeber strength. Changes in the structural symmetry of the system indicated that these results are expected for a wide range of system configurations, while reproduction of the same phenomena with a simpler model, considering phase effects only, added to the generality of conclusions. We argue that our modeling approach can serve as a conceptual framework for understanding, planning and interpreting conflicting zeitgeber experiments. Work done in collaboration with Daniel S.C.Damineli and Andreas Bohn (Universidade Nova de Lisboa) and W. Otto Friesen (University of Virginia).