Heat waves are a major cause of weather-related deaths. With the current concern for global warming it is reasonable to suppose that they may increase in frequency, severity, duration, or areal extent in the future. However, in the absence of an adequate definition of a heat wave, it is impossible to assess either changes in the past or possible consequences for the future. A set of definitions is proposed here, based on the criteria for heat stress forecasts developed by the National Weather Service (NWS). Watches or warnings are issued when thresholds of daytime high and nighttime low heat index (Hi) values are exceeded for at least two consecutive days. The heat index is a combination of ambient temperature and humidity that approximates the environmental aspect of the thermal regime of a human body, with the NWS thresholds representing a generalized estimate of the onset of physiological stress. These thresholds cannot be applied directly nationwide. In hot and humid regions, physical, social, and cultural adaptations will require that the thresholds be set higher to ensure that only those events perceived as stressful are identified. In other, cooler, areas the NWS criteria may never be reached even though unusually hot events may be perceived as heat waves. Thus, it is likely that a similar number of perceived heat events will occur in all regions, with the thresholds varying regionally. Hourly Hi for 178 stations in the coterminous United States was analyzed for the 1951-90 period to determine appropriate threshold criteria. Use of the NWS criteria alone indicated that much of the nation had less than three heat waves per decade, and this value was adopted as the baseline against which to establish suitable thresholds. For all areas, a percentile threshold approach was tested. Using all available data, daytime high and nighttime low thresholds were established separately for each specific percentile. Heat waves were treated as occurring when conditions exceeded both the daytime high and the nighttime low thresholds of the same percentile for two consecutive days. Several thresholds were tested. For much of the South, 1% thresholds produced appropriate values. Consequently, a heat wave was defined as a period of at least 48 h during which neither the overnight low nor the daytime high Hi falls below the NWS heat stress thresholds (80° and 105°F, respectively), except at stations for which more than 1% of both the annual high and low Hi observations exceed these thresholds, in which case the 1% values are used as the heat wave thresholds. As an extension, `hot spells' were similarly defined, but for events falling between the 1% values and NWS thresholds, with `warm spells' occurring between the 2% and 1% values. Again, stations for which the 1% or 2% Hi values exceed the NWS thresholds were given modified definitions. The preliminary investigation of the timing and location of heat waves resulting from these definitions indicated that they correctly identified major epidemiological events. A tentative climatic comparison also suggests that heat waves are becoming less frequent in the southern and more frequent in the midwestern and eastern parts of the nation.