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The network concept is increasingly used for the description of complex systems. Here, we summarize key aspects of the evolvability and robustness of the hierarchical network set of macromolecules, cells, organisms and ecosystems. Listing the costs and benefits of cooperation as a necessary behaviour to build this network hierarchy, we outline the major hypothesis of the paper: the emergence of hierarchical complexity needs cooperation leading to the ageing (i.e. gradual deterioration) of the constituent networks. A stable environment develops cooperation leading to over-optimization, and forming an 'always-old' network, which accumulates damage, and dies in an apoptosis-like process. A rapidly changing environment develops competition forming a 'forever-young' network, which may suffer an occasional over-perturbation exhausting system resources, and causing death in a necrosis-like process. Giving a number of examples we demonstrate how cooperation evokes the gradual accumulation of damage typical to ageing. Finally, we show how various forms of cooperation and consequent ageing emerge as key elements in all major steps of evolution from the formation of protocells to the establishment of the globalized, modern human society.