Cooperation between human operators and autonomous machines in dynamic (not fully controlled) situations implies a need for dynamic allocation of activities between the agents. Depending on whether tasks or functions are allocated, the demands made on human-machine cooperation design are different. Task and Subtask allocation assumes that both the human operator and the machine (or its designer) share the same decomposition of the overall task into subtasks. Function delegation is less demanding, provided that the human operator delegates functions to the machine explicitly, and within the context of a task representation transmitted by the human. This paper uses an example taken from a series of studies on human-machine cooperation in air traffic control in order to illustrate its argument.