The need for energy efficient, clean and quiet, energy conversion devices for mobile and stationary applications has presented proton exchange membrane (PEM) fuel cells as a potential energy source. The use of PEM fuel cells for automotive and other transient applications, where there are rapid changes in load, presents a need for better understanding of transient behavior. In particular at low humidity operations; one of the factors critical to the performance and durability of fuel cell systems is water transport in various fuel cell layers, including water absorption in membrane. An essential aspect to optimization of transient behavior of fuel cells is a fundamental understanding of response of fuel cell system to dynamic changes in load and operating parameters. This forms the first objective of the dissertation. An insight in to the time scales associated with various transport phenomena will be discussed in detail. In the second component on the study, the effects of membrane properties on the dynamic behavior of the fuel cells are analyzed with focus on membrane dry-out for low humidity operations. The mechanical behavior of the membrane is directly related to the changes in humidity levels in membrane and is explored as a part third objective of the dissertation. Numerical studies addressing this objective will be presented. Finally, porous media undergoing physical deposition (or erosion) are common in many applications, including electrochemical systems such as fuel cells (for example, electrodes, catalyst layer s, etc.) and batteries. The transport properties of these porous media are a function of the deposition and the change in the porous structures with time. A dynamic fractal model is introduced to describe such structures undergoing deposition and, in turn, to evaluate the changes in their physical properties as a function of the deposition. / Ph. D.