In this paper, a new project scheduling problem is introduced, the periodically aggregated resource-constrained project scheduling problem (PARCPSP), in which the resource usage is considered on average over aggregated periods of parameterised length, while temporal aspects (start/completion dates of activities and precedence relations) are taken into account in an exact manner. A mixed integer linear programming formulation based on a mixed time representation is given. The adaptation of schedule generation schemes developed for standard project scheduling problems is discussed. An iterative solution scheme is described; experiments show that this method permits to find better upper bounds and sometimes enables to reduce the overall computational time.