The capabilities of Business Process Management Systems (BPMS's) are continuously extended to increase the effectiveness of the management and enactment of business processes. This paper identifies the challenge of case prediction, which for a specific case under the control of a BPMS deals with the estimation of the remaining time until it is completed. An accurate case prediction facility is a valuable tool for the operational control of business processes, as it enables the pre-active monitoring of time violations. Little research has been carried out in this area and few commercial tools support case prediction. This paper lists the requirements on such a facility and sketches some directions to reach a solution. To illustrate the depth...