Polyelectrolyte gels have the ability to undergo volume transitions in response to external stimuli. As a result, they are used in a wide variety of applications such as sensors, actuators, artificial implants, and controlled drug delivery. In addition, diffusion of trapped macromolecules inside gels is of tremendous significance in drug delivery systems. In this thesis, the dynamics of trapped polyelectrolytes in a polyelectrolyte gel is studied using dynamic light scattering technique. The effect of the crosslink density and the charge density of the gel, as well as of solvent quality and salt concentration are investigated. In general, two distinct diffusive modes (fast and slow) are observed in light scattering experiments. We have discovered that the fast mode corresponds to the gel elasticity and the slow mode corresponds to diffusion of trapped polymer. The deduced diffusion coefficient of the trapped polymer obeys an exponential dependence on the volume fraction of the gel, in accordance with the presence of an entropic barrier for polymer diffusion. In addition, we have monitored the diffusion of a neutral polymer in polyelectrolyte gels using fluorescence correlation spectroscopy. We demonstrate that the polymer diffusion is considerably slowed down by the gel due to the coupling between polymer dynamics and gel dynamics.