Operation of PEM fuel cells (PEMFC) with the dead-ended anode (DEA) leads to severe voltage transients due to accumulation of nitrogen, water vapor and liquid water in the anode channels and the gas diffusion layer (GDL). Accumulation of nitrogen causes a large voltage transient with a characteristic profile whereas the amount of water vapor in the anode is limited by the saturation pressure, and the liquid water takes up very small volume at the bottom of the anode channels in the case of downward orientation of the gravity. We present a transient 1D along-the-channel model of PEMFCs operating with periodically-purged DEA channels. In the model, transport of species is modeled by the Maxwell-Stefan equations coupled with constraint equations for the cell voltage. A simple resistance model is used for the permeance of nitrogen and transport of water through the membrane. Simulation results agree very well with experimental results for voltage transients of the PEMFC operating with the DEA. In order to emphasize the effect of nitrogen accumulation in the anode, we present experimentally obtained cell voltage measurements during DEA transients when the cathode is supplied with pure oxygen. In the absence of nitrogen in the cathode, voltage remained almost constant throughout the transient. The model is used to demonstrate the effect of oxygen-to-nitrogen feed ratio in the cathode on the voltage transient behavior for different load currents. Lastly, the effect of small leaks from the anode exit on the voltage transient is studied: even for leak rates as low as 10 ml/h, nitrogen accumulation in the anode channels is alleviated and the cell voltage remained almost constant throughout the transient according to the results.