In the quest for obtaining accurate closed-form analytical expressions for polarization curve of a proton exchange membrane fuel cell (PEMFC), we have recently presented a two-dimensional model that accounts for oxygen concentration gradient and velocity gradient along the depth of a cathode flow channel. The model was developed for the case when Tafel kinetics of oxygen reduction reaction (ORR) on the cathode governs the overall rate of oxygen consumption. An improved match between predictions of the model and full three-dimensional simulations was obtained over the entire range of current density compared with earlier models which assumed homogenous oxygen concentration in the channel depth and plug flow velocity profile. In reality however, ORR kinetics is often not the rate limiting step for oxygen consumption in the cathode catalyst layer (CCL) at high current density since the Tafel kinetics is modulated by transport resistances in the CCL. In this article, we extend our two-dimensional analytical model to two different transport-limited regimes of CCL operation namely, slow oxygen transport across the CCL and slow proton transport across the CCL. We compare model predictions with results of full three-dimensional simulations in both cases and show that they are in excellent agreement even in these transport limited operational regimes of PEMFC. (C) 2018 Elsevier Ltd. All rights reserved.