Consider an overloaded, multiclass queueing system with abandonment. The single server visits the queues in a cyclic, round robin fashion and processes a class‐specific number of jobs at each visit, if possible. We prove a limit theorem for the K‐dimensional queue length process. Classes are grouped by whether capacity relative to them is effectively over‐, under‐, or critically‐loaded. Equivalence is shown between generalized round robin and generalized processor sharing policies.