This paper presents the development of a nonlinear state observer to estimate the different gas species concentration profiles in a Proton Exchange Membrane Fuel Cell energy system. The selection of the estimated states follows functionality and fuel cell performance criteria. The implementation is based on the finite element discretisation of a fuel cell distributed parameter model. Forward and backwards discretisation of the partial derivative equations is performed to take advantage of the boundary conditions of the problem and also to apply lumped systems theory in the synthesis procedure of the observer. A second-order sliding-mode super-twisting corrective input action is implemented to reduce the estimation error to zero in a finite amount of time. The sliding-mode control approach grants a suitable corrective action without incrementing the model-dependency of the observer. Simulation results are presented to show the performance of the proposed observer of the fuel cell internal states and to extract conclusions for future research work. Peer Reviewed