A new model for hard-real-time tasks - the recurring branching task model - is introduced, which is capable of modelling some restricted forms of conditional real-time process code. This model generalizes earlier models such as the sporadic task model and the generalized multiframe task model. It is shown that feasibility analysis in this model - determining whether a system of several recurring branching tasks that share a processor can all be scheduled to always meet all deadlines - can be performed efficiently, in pseudo-polynomial time.