This paper investigates the stability domain of ferroresonance in asymmetric three-phase three-leg transformers considering magnetic couplings and hysteresis effects of the core. A newly developed and accurate time-domain transformer model capable of simulating dynamic and transient operating conditions is implemented in this study. The model is based on electromagnetic circuit theory and considers dynamic hysteresis effects (major and minor loops) as well as core topology, asymmetry, and magnetic flux cross-coupling interactions of the core legs. Unbalanced switching with series and shunt capacitances, which is known to increase the risk of ferroresonance, is studied with the developed model. The validity of the model under ferroresonant conditions is confirmed by comparisons with extensive experimental data. The main contribution is a new analysis of (a) symmetric three-phase transformer ferroresonance behavior with an accurate core model capable of predicting ferroresonance modes.