In this paper we introduce a new task model that is specifically targeted towards representing stream processing applications. Examples of such applications are those involved in network packet processing (such as a software-based router) and multimedia processing (such as an MPEG decoder application). Our task model is made up of two parts: (i) a new task structure to accurately model the software structures of stream processing applications such as conditional branches and different end-to-end deadlines for different types of input data items, and (ii) a new event model to represent the arrival pattern of the data items to be processed, which triggers the task structure. This event model is more expressive than classical models such as purely periodic, periodic with jitter or sporadic event models. We then present algorithms for the schedulability analysis of this task model. The basic scheme underlying our algorithms is a generalization of the techniques used for the schedulability analysis of the recently proposed generalized multiframe and the recurring real-time task models.