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The luminosity of stripped-envelope supernovae, a common type of stellar explosion, is believed to be mainly driven by the radioactive decay of the nickel synthesized in the explosion and carried in its ejecta. Additional possible energy sources have been previously suggested1–5, in which the two most observationally based results have been from a comparison of the observed time-weighted luminosity with the inferred radioactive power1 and from a comparison of the light curves with particular theoretical models3. However, the former result1 was not statistically significant, and the latter3 is highly dependent on the specific models assumed. Here we analyse the energy budget of a sample of 54 well-observed stripped-envelope supernovae of all sub-types and present statistically significant, largely model-independent, observational evidence for a non-radioactive power source in most of them (and possibly in all). We consider various energy sources, or alternatively, plausible system ....