  Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetimes, are
examined with regard to their stability, and compared with similar orbits in
the near-extremal situation. Extremization of the effective potential for null
circular orbits shows the existence of a stable circular geodesic in the
extremal spacetime, precisely {\it on} the event horizon, which coincides with
its null geodesic generator. Such an orbit also emerges as a global minimum of
the effective potential for circular {\it timelike} orbits. This type of
geodesic is of course absent in the corresponding near-extremal spacetime, as
we show here, testifying to differences between the extremal limit of a generic
RN spacetime and the exactly extremal geometry.
