The immune system has many adaptive and dynamic components that are regulated to ensure appropriate, precise and rapid response to a foreign pathogen. A delayed or inadequate immune response can lead to prolonged disease, while an excessive or under-regulated response can lead to autoimmunity. The cytokine, interleukin-2 (IL-2) and its receptor IL-2R play an important role in maintaining this balance.The IL-2 receptor transduces pSTAT5 signal through both the intermediate and high affinity receptors, which differ from each other by the presence of CD25 chain in IL-2 receptor. We present experimental data on the kinetics of pSTAT5 signalling through both of the receptors and develop a model that captures this kinetics. We then use this model to parameterize key aspects of two additional models in which we propose and study two different mechanisms by which IL-2 receptor can transduce distinct signals leading to either an activated or a non-activated cell state. We speculate that this initial state differentiation, perhaps enhanced by downstream feedbacks, may eventually lead to differential cell fates.Our result shows that non-linear dynamical models can suggest resolution of a puzzling array of seemingly contradictory experimental results on IL-2 effect on proliferation and differentiation of T-cells.