In order to understand the origin of long-lived loci of volcanism (sometimes called "hot spots") and their possible role in global tectonic processes, it is essential to know their deep structure. Even though some work has been done on the crustal, upper-mantle, and deep-mantle structure under some of these "hot spots", the picture is far from clear. In an attempt to study the structure under the Yellowstone National Park U.S.A., which is considered to be such a "hot spot", we recorded teleseisms using 26 telemetered seismic stations and three groups of portable stations. The network was operated within a 150 km radius centered on the Yellowstone caldera, the major, Quaternary volcanic feature of the Yellowstone region. Teleseismic delays of about 1.5 sec are found inside the caldera, and the delays remain high over a 100 km wide area around the caldera. The spatial distribution and magnitude of the delays indicate the presence of a large body of low-velocity material with horizontal dimensions corresponding approximately to the caldera size (40 km ?? 80 km) near the surface and extending to a depth of 200-250 km under the caldera. Using ray-tracing and inversion techniques, it is estimated that the compressional velocity inside the anomalous body is lower than in the surrounding rock by about 15% in the upper crust and by 5% in the lower crust and upper mantle. It is postulated that the body is partly composed of molten rock with a high degree of partial melting at shallow depths and is responsible for the observed Yellowstone volcanism. The large size of the partially molten body, taken together with its location at the head of a 350 km zone of volcanic propagation along the axis of the Snake River Plain, indicates that the volcanism associated with Yellowstone has its origin below the lithosphere and is relatively stationary with respect to plate motion. Using our techniques, we are unable to detect any measurable velocity contrast in the mantle beneath the low-velocity body, and, hence, we are unable to determine whether the Yellowstone melting anomaly is associated with a deep heat source or with any deep phenomenon such as a convection plume, chemical plume, or gravitational anchor. ?? 1979.