Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or reenter the queue, possibly as customers of a different class. The server is operating under the egalitarian processor sharing discipline. Building on prior work by Gromoll et al. and Puha et al., we establish the convergence of a properly normalized state process to a fluid limit. We show the existence of a unique solution to this fluid limit model, both for a stable and an overloaded queue. We also describe the asymptotic behavior of the trajectories of the fluid limit.