Doppler spectroheliograms of sunspots and their surroundings have been obtained with a spatial resolution approaching one second of arc and a time resolution of 20 s per frame. Observations of 5 sunspots, located 18 ~ 45 ~ 56 ~ 60 ~ and 72 ~ from the disk center respectively, showed considerable long-lived fine structure and, in particular, indicated the following:(1) The Evershed outflow terminated in spoke-like structures that constitute the ragged outer boundary of the penumbra. Some of these spokes extended more than 8000 km beyond the average outer boundary.(2) Although there was considerable long-lived fine structure of both Doppler polarities in the extra-penumbral photosphere, the spatially-averaged horizontal flow was outward for roughly I0000 km beyond the outer boundary of the penumbra. This extra-penumbral velocity field was distinct from the Evershed flow, and, in particular, did not represent its extension beyond the end of the penumbral spokes.Although these results are based on observations of relatively few sunspots, they do suggest that if magnetic fields are carried outward from sunspots by material motions, then these motions are more like the supergranulation than an extension of the Evershed velocity.