Electric fields with amplitudes to 140 mV/m and average durations of 7.5 milliseconds have been observed at the magnetospheric side of the dayside magnetopause. These fields are predominantly perpendicular to B, they are electrostatic, and they occur inside local minima in the plasma density. Because they have been observed at each of approximately seven opportunities, they must be a common feature of the magnetopause. They may be associated with the magnetospheric separatrix because computer simulations suggest such structures. Their complete characterization requires time domain measurements of plasma and three component fields with better than a few millisecond time resolution.