Present-day knowledge concerning the molecular structure of supercritical fluids is briefly reviewed. It is shown that liquid-like and gas-like phases may coexist at supercritical pressures, although they may not be in equllibrium with each other. it is postulated that on the basis of the coexistence of these two phases a "boiling-like" phenomenon may provide the mechanism of heat transfer to supercritical fluids at high heat fluxes and certain other conditions. An unusual mode of heat transfer was actually observed at supercritical pressures during tests which produced the high heat fluxes and other conditions under which such "boiling" would be expected. The tests and the various conditions are briefly described. An emission of high-frequeney, high-intensity sounds usually accompanied these tests. It is shown that similar screaming sounds were heard during boiling at subcritical pressures, giving further support to the hypothesis that "boiling" may occur at supercritical pressures. A seeond possible explanation for the unusual mode of heat transfer is based on boundarylayer stability considerations. At high heat fluxes large density differences exist between the bulk of the fluid and the fluid in the boundary layer near the wall. A breakdown of the boundary layer may be caused by the build-up of …