Copepods, the small planktonic crustaceans that are the most abundant metazoans in the oceans, are so successful partly because they have an escape response that accelerates them to 200 body lengths per second within milliseconds1,3. We find that nerve fibres of many copepods seem to be designed for rapid signalling. They have well-developed myelin-like sheaths, like those that give a tenfold boost to the conduction speed of nerve impulses in vertebrates4. By reducing a copepod's reaction time to predatory attack, these sheaths may be crucial to the survival of the large copepod populations that inhabit dangerous oceanic ecosystems.