A processing system comprises plural processing cores and a task allocator for allocating tasks to the processing cores. The processing cores perform the tasks that are allocated to them so as to produce results for the tasks, the results being stored by the processing cores in a buffer. The task allocator indicates to the processing cores memory portions within the buffer in which to store the results. When the processing cores determine that a given memory portion is becoming full, the processing cores request that the task allocator indicates a new memory portion in which to store its results. The processing system allows the task allocator to dynamically and efficiently allocate memory portions to plural processing cores without the task allocator 40 needing to know the sizes of the results being produced by the processing cores.