Runaway electron orbits are calculated in a tokamak magnetic field. It is shown that these electrons tend to drift towards a larger major radius with a velocity = qcE/B0R. This effect may be relevant to some recent experimental observations in tokamaks, namely, the correlation between the loop voltage and the hard-X-ray flux in lower-hybrid-wave current-drive experiments and the exceptionally long plasma life-time in a low-density, low-loop-voltage tokamak discharge.