The transient behavior of the single server queue under the processor sharing discipline is analysed. The rate of growth of the number of customers in the queue as well as the asymptotic behavior of the residual service times described in terms of a renormalized point process are given. The analysis of the queue of the customers is done under general assumptions. The results are obtained under the hypothesis of stationary arrival process and stationary sequence of service times. The customers arrive according to a stationary ergodic marked point process, its Palm probability measure attached to. It is assumed that the workload of the transient single server queue grows at rate \(\lambda E(\sigma_ 0) - 1>0\), where \(\lambda\) is the arrival rate and \(E(\sigma_ 0)\) the expected value of the service time.