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G\"{u}del and Benz (1993, ApJ 405, L63) have found a linear relationship between the ``quiescent'' X-ray and microwave emissions from a broad range of active stars. Since the microwave emission is almost certainly from nonthermal electrons, this indicates a close relationship between coronal heating and particle acceleration in these stars. I will show that Joule heating and the simultaneous acceleration of runaway electrons in current channels provides this relationship. The implications for the physical conditions in stellar coronae will be discussed.