Two different one dimensional, time dependent models are developed to study transient phenomena in railgun plasma armatures. The first model consists of the equations for conservation of mass and momentum, and the magnetic diffusion equation for an isothermal plasma. The second, more general model eliminates the assumption of an isothermal arc, and allows for the generation and transfer of hear within the armature. This requires that the conservation equations be supplemented by an energy equation. Validation of this isothermal model is achieved by comparing the long time behavior of numerical solutions to known analytic solutions. It is exercised to study the evolution of a plasma armature from a stationary steady-state to and to provide an estimate for the relaxation time. Simulation of the initiation of a plasma armature from an exploding foil in contact with the projectile with the isothermal model indicates that the initiation process strongly influences the dynamics of the arc/projectile system at early times. The more general armature model is applied to the study of the transient processes which occur when an armature collides with a projectile. Our preliminary calculations indicate the utility of the model in helping to understand transient phenomena. Several possible techniques for reducing the computation time of the general model are identified. The implications of these results on the performance of railguns, as well as plans for future analyses, are discussed.