Autoregulation and nucleocytoplasmic shuttling play important roles in the operation of the GAL regulatory system. However, the significance of these mechanisms in the overall operation of the switch is unclear. In this work, we develop a dynamic model for the GAL system and further validate the same using steady-state and dynamic experimental expression data. Next, the model is used to delineate the relevance of shuttling and autoregulation in response to inducing, repressing, and non-inducing-non-repressing media. The analysis indicates that autoregulation of the repressor, Gal80p, is key in obtaining three distinct steady states in response to the three media. In particular, the analysis rationalizes the intuitively paradoxical observation that the concentration of repressor, Gal80p, actually increases in response to an increase in the inducer concentration. On the other hand, although nucleocytoplasmic shuttling does not affect the dynamics of the system, it plays a dominant role in obtaining a sensitive response to galactose. The dynamic model was also used to obtain insights on the preculturing effect on the system behavior.